Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system | Paper Citation Record

Observation 50d5252b-aa4d-4c10-a13d-66bfc536015e · outbound

This paper cites Abramovitz and I.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Abramovitz and I

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-05T21:48:35.241759Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8eb01ad3-379b-4bb9-9055-1cfa01a05ae1 · outbound

This paper cites Biler Local and global solvability of some parabolic systems modelling chemotaxis , , Adv.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Biler Local and global solvability of some parabolic systems modelling chemotaxis , , Adv

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-05T21:48:35.404070Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 01b5188e-fc7e-4c4b-b869-b81c3085454f · outbound

This paper cites Biler, G.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Biler, G

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-05T21:48:35.524735Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c343f76e-ef07-4f39-86af-8a92cf7b3b01 · outbound

This paper cites Biler, G.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Biler, G

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-05T21:48:35.636625Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8aebbc70-1aa4-46ec-b4f6-d0b0e939d9d4 · outbound

This paper cites Blanchet On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher , S ´eminaire Laurent Schwartz—Equations aux d´eriv´ees partielles et applications.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Blanchet On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher , S ´eminaire Laurent Schwartz—Equations aux d´eriv´ees partielles et applications

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:49:03.327744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 4a332ae7-3f15-41ad-a585-e44a53a1bfa9 · outbound

This paper cites Blanchet, E.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Blanchet, E

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:49:03.028649Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2f86ecb6-f7d2-4313-bfe5-46676ad9a94e · outbound

This paper cites Blanchet, J.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Blanchet, J

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:49:02.782505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation cde11ee4-ffaf-4788-a104-d9a0f7f968fa · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:49:02.468364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f245901c-ca29-4725-a7ba-6b954fa673e9 · outbound

This paper cites Blanchet, J.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Blanchet, J

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:49:02.239971Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c602cad1-ad43-41e9-a635-251ab700e5c3 · outbound

This paper cites Existence of finite time blow-up in Keller-Segel system.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Existence of finite time blow-up in Keller-Segel system

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-05T21:48:36.390748Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b7b08a1a-f11e-443a-ad4a-e9ba7200f620 · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:49:02.044537Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 099065c8-3518-4287-bcef-748e41c6c1b2 · outbound

This paper cites Campos & J.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Campos & J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:49:01.741704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a3b4f2d0-413e-4992-b7f3-a1e014b98bbb · outbound

This paper cites Campos & J.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Campos & J

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:49:01.536506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 917ce00a-0a0e-4a98-aeb8-8094fe0c687c · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:49:01.316661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 4e97ad6c-ddd6-4ccd-8fa3-2ab1a86e811c · outbound

This paper cites Carlen & M.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Carlen & M

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:49:01.088282Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 73cf0315-dcb7-4bb8-8c53-662e6bb9c305 · outbound

This paper cites Carlen & A.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Carlen & A

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:49:00.848675Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 70cde265-d372-4f42-91f4-1e113c1300aa · outbound

This paper cites Chavanis, Nonlinear mean field Fokker-Planck equations.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Chavanis, Nonlinear mean field Fokker-Planck equations

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:49:00.663904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 0984bc71-9909-4539-b6ba-c7811b304cd1 · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:49:00.409602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3be7286e-8b54-4518-aaff-3deb31e0b503 · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:49:00.154140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 076a47e9-25d2-4120-ad11-b754fd3f3b20 · outbound

This paper cites Childress & J.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Childress & J

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:59.868297Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 7f53aa3c-8884-4079-86b0-74946cad2497 · outbound

This paper cites Collot, T.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Collot, T

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:59.582642Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3e445d83-bfec-44fc-a3af-11c232fa6d9a · outbound

This paper cites Collot, T.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Collot, T

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:59.313860Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e3b072a4-08d4-483c-9a49-df5ca46a4e4c · outbound

This paper cites Collapsing-ring blowup solutions for the Keller-Segel system in three dimensions and higher.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Collapsing-ring blowup solutions for the Keller-Segel system in three dimensions and higher

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-05T21:48:44.714538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ccfa7e61-9e87-412d-b1ee-b87d519190bd · outbound

This paper cites On the stability of Type I self-similar blowups for the Keller-Segel system in three dimensions and higher.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system On the stability of Type I self-similar blowups for the Keller-Segel system in three dimensions and higher

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-05T21:48:37.846714Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cee8237c-0e16-467d-986c-1de54c04425e · outbound

This paper cites Corrias, B.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Corrias, B

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:59.066414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 5cb464fa-a72b-4f86-a172-62c5481687e2 · outbound

This paper cites Corrias, V.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Corrias, V

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:58.779196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ca6b37e4-c59d-430d-9144-52aa2810f26c · outbound

This paper cites Cort´ azar, M.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Cort´ azar, M

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:58.489687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 78a02d48-6d33-4ff3-b175-4e8adf0446ab · outbound

This paper cites Existence and stability of infinite time blow-up in the Keller-Segel system.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Existence and stability of infinite time blow-up in the Keller-Segel system

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-08-05T21:48:44.535082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b02cf0e8-93f9-4823-ae7f-d66992a25374 · outbound

This paper cites D´ avila, M.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system D´ avila, M

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:58.241273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d597d0e1-9e69-4acd-9bf2-eee31bdc5c49 · outbound

This paper cites D´ avila, M.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system D´ avila, M

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:57.973319Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b9eab7f9-9604-46fc-a332-e930d6d99fa9 · outbound

This paper cites D´ avila, M.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system D´ avila, M

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:57.635315Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 0108073d-5312-4802-977e-9d40090dc1b3 · outbound

This paper cites D´ avila, M.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system D´ avila, M

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:57.415664Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 18989f16-96cd-4dc2-a455-679e864d61cd · outbound

This paper cites Dejak, P.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Dejak, P

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:57.162699Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 4813cb1b-e981-43a7-a006-bc11c63cc250 · outbound

This paper cites del Pino Bubbling blow-up in critical parabolic problems, in Nonlocal and nonlinear diffusions and interactions: new methods and directions , vol.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system del Pino Bubbling blow-up in critical parabolic problems, in Nonlocal and nonlinear diffusions and interactions: new methods and directions , vol

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:56.916053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d5e56aff-5884-4dc5-862a-ac6a3dca9041 · outbound

This paper cites del Pino, M.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system del Pino, M

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:56.637255Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 7940be9a-443e-44cb-91d9-75d7e47ad070 · outbound

This paper cites del Pino & J.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system del Pino & J

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:56.421982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a40679f5-813e-4d24-964c-e9f6c8eefb39 · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:56.079297Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f5184dd9-160b-46f9-a98e-15e33345627d · outbound

This paper cites Dolbeault & B.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Dolbeault & B

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:55.871401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 472e6d0b-2333-49a6-89b8-1c36fd6860b8 · outbound

This paper cites Dolbeault & C.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Dolbeault & C

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:55.554166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1cdf9550-f4ea-4548-b14c-6e0767f4836e · outbound

This paper cites Ega˜ na Fern´ andez & S.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Ega˜ na Fern´ andez & S

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:55.274768Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 047c5799-b453-4893-992a-682b7af14e21 · outbound

This paper cites Ghoul & N.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Ghoul & N

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:54.975351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 4c30344f-b7a6-40d4-81d6-dd3d848962bf · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:54.728321Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a97a0156-d0f2-47c4-8801-f6e0626fe6a9 · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 43

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:54.431515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1b5b973f-f253-4a9f-9ba2-779b4d3225c5 · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:54.168547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 8f3b03f2-6e97-40a2-b080-111c6ccfc852 · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 45

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:53.863242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b4f51fb0-fa11-4fda-8a65-37822cb6b6bb · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:53.616035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 96464a0d-096a-4e9c-aa1b-6d2fdbda9c6d · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 47

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:53.283045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 198374a9-d510-442b-a7a2-acd2a9b3fe82 · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 48

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:53.043276Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ce44754a-ba74-4bee-bb47-96134494d557 · outbound

This paper cites Hillen & K.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Hillen & K

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:52.783552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation df6f8fc4-e652-43f9-8642-b9122c87fa1e · outbound

This paper cites Horstmann From 1970 until present: the Keller-Segel model in chemotaxis and its consequences.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Horstmann From 1970 until present: the Keller-Segel model in chemotaxis and its consequences

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:52.508960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2f5447fb-5d78-448e-a981-4f10ba636c05 · outbound

This paper cites Horstmann From 1970 until present: the Keller-Segel model in chemotaxis and its consequences.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Horstmann From 1970 until present: the Keller-Segel model in chemotaxis and its consequences

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:52.204098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f305a1f1-9913-4053-8da7-bacac7f28e4d · outbound

This paper cites Axisymmetric type II blowup solutions to the three-dimensional Keller-Segel system.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Axisymmetric type II blowup solutions to the three-dimensional Keller-Segel system

Reference 52

Resolution: verified exact; local_arxiv, observed 2026-08-05T21:48:44.298831Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation bb9a95a9-040e-4390-87b2-4bcc08ac4f5c · outbound

This paper cites J¨ ager & S.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system J¨ ager & S

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:51.998888Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b4064c91-c49b-4692-88e8-562e60280a80 · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 54

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:51.766090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d82d397a-80b3-43b1-b7a7-bb5c6a7daa7b · outbound

This paper cites Karp & S.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Karp & S

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:51.572441Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 711a324c-4890-41b9-a0ca-2d146fa6ee4c · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 56

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:51.399612Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 943b5b8c-ad06-4c0e-aeae-0d6ccdb0cf38 · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 57

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:51.186634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f28e773a-3eb5-4bf4-99f5-c03dc1864c3e · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 58

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:50.882674Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e37dfcfa-3d05-42a9-af44-70d40d00eede · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 59

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:50.700404Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d5a518b1-2322-4f1e-b4c8-57aeacd12a8c · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 60

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:50.490904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d9878c31-bfda-48ef-bc6f-bc12d84c2f89 · outbound

This paper cites Kozono & Y.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Kozono & Y

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:50.139808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 18af0467-5150-460b-8426-b1ff14469bb3 · outbound

This paper cites Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-05T21:48:41.642972Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b995dbda-d244-4cb0-a14a-aa66bcffb712 · outbound

This paper cites L´ opez-G´ omez, T.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system L´ opez-G´ omez, T

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:49.907688Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 09709a66-3095-411c-9be4-3a3e6f70fb49 · outbound

This paper cites L´ opez-G´ omez, T.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system L´ opez-G´ omez, T

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:49.647360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 278301b5-6b15-4125-aa30-85dfa8b6255a · outbound

This paper cites Mizoguchi Refined asymptotic behavior of blowup solutions to a simplified chemotaxis system.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Mizoguchi Refined asymptotic behavior of blowup solutions to a simplified chemotaxis system

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:49.430679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e05fb798-fc91-4786-be02-6379b2f02ee4 · outbound

This paper cites Nagai Blow-up of radially symmetric solutions to a chemotaxis system.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Nagai Blow-up of radially symmetric solutions to a chemotaxis system

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:49.109886Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 910df993-c0e0-4277-bb07-0e134113b8f4 · outbound

This paper cites Nagai Blowup of nonradial solutions to parabolic–elliptic systems modeling chemotaxis in two-dimensional domains, Journal of Inequalities and Applications, 2001 (2001), p.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Nagai Blowup of nonradial solutions to parabolic–elliptic systems modeling chemotaxis in two-dimensional domains, Journal of Inequalities and Applications, 2001 (2001), p

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:48.768099Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b16258f1-756d-416b-ae92-547f3dc6cb0e · outbound

This paper cites Nagai Convergence to self-similar solutions for a parabolic-elliptic system of drift-diffusion type in R2, Adv.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Nagai Convergence to self-similar solutions for a parabolic-elliptic system of drift-diffusion type in R2, Adv

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:48.493454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c829bacc-1671-4cd9-87aa-641409ab80a6 · outbound

This paper cites Nagai & T.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Nagai & T

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:48.252540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e411f9bf-f166-4599-9562-f752ff2f86ca · outbound

This paper cites Nagai & T.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Nagai & T

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:47.990825Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 725b2c77-cce6-4d49-bd72-8d86680ca4e6 · outbound

This paper cites Nanjundiah, Chemotaxis, signal relaying and aggregation morphology , Journal of Theoretical Biology, 42(1):63 – 105, 1973.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Nanjundiah, Chemotaxis, signal relaying and aggregation morphology , Journal of Theoretical Biology, 42(1):63 – 105, 1973

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:47.720574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a712fb59-bedd-483e-8be4-4fc413980fb6 · outbound

This paper cites Construction of type I-Log blowup for the Keller-Segel system in dimensions $3$ and $4$.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Construction of type I-Log blowup for the Keller-Segel system in dimensions $3$ and $4$

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-05T21:48:42.762538Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7143631e-7dad-46ba-96a9-7aa6e58d74b6 · outbound

This paper cites Nishihara, A note on the stability of travelling wave solutions of Burgers’ equation , Japan J.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Nishihara, A note on the stability of travelling wave solutions of Burgers’ equation , Japan J

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:47.497623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 47752c3a-7acf-45fb-b5c5-61cbf1eeb8cb · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 74

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:47.291545Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 7bbfabe7-20a6-4abc-aeb1-bfa9b0731114 · outbound

This paper cites Rapha¨ el & R.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Rapha¨ el & R

Reference 75

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:47.062129Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 544d5104-e16a-4aa6-a5ea-ef005664baee · outbound

This paper cites Senba, Blowup behavior of radial solutions to J¨ ager-Luckhaus system in high dimensional domains , Funkcialaj Ekvacioj, 48(2):247–271, 2005.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Senba, Blowup behavior of radial solutions to J¨ ager-Luckhaus system in high dimensional domains , Funkcialaj Ekvacioj, 48(2):247–271, 2005

Reference 76

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:46.864746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ddc57107-be2d-4f66-8c4a-a4fa5c3409a9 · outbound

This paper cites Senba & T.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Senba & T

Reference 77

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:46.706542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b294ccf9-2565-4b26-ac8f-3bf91412b94d · outbound

This paper cites Sire & P.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Sire & P

Reference 78

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:46.458706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2f22fa61-da3c-4f8d-919b-e7ba561bf805 · outbound

This paper cites Souplet & M.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Souplet & M

Reference 79

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:46.286750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation cd7c44cb-2391-45d0-b8aa-ea34103ba319 · outbound

This paper cites Van de Vel On the series expansion method for computing incomplete elliptic integrals of the first and second kinds., Math.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Van de Vel On the series expansion method for computing incomplete elliptic integrals of the first and second kinds., Math

Reference 80

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:46.022152Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d77044ba-9f63-4dd2-8991-fa72ae7f26e0 · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 81

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:45.773898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 11eabd16-5b81-4a87-a12b-f4f8ffc647c0 · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 82

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:45.563388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation aa1317fb-f29b-4627-b70d-a9ebcad24c46 · outbound

This paper cites an unresolved cited work.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Unresolved cited work

Reference 83

Resolution: unresolved; raw_fallback, observed 2026-08-05T21:48:45.264820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 972b7d50-bf89-41e0-84f4-ab2991761f0c · outbound

This paper cites Wolansky, On steady distributions of self-attracting clusters under friction and fluctuations.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Wolansky, On steady distributions of self-attracting clusters under friction and fluctuations

Reference 84

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T21:48:44.980814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Reference resolution

Outbound references

Pith citing papers