Paper Citation Record · LEDGER

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations

As of 20 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2608.12226.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2608.12226 v1

Coverage vector

measured 32 of 32 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-16T00:24:30.331979Z

measured 32 of 32 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

32 of 32 outbound references displayed

verified exact3
verified fuzzy22
unresolved7
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External citation measurements

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Outbound references

Observation 79744360-b27f-4057-be00-5d782e30397b · outbound

This paper cites Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-16T00:24:30.686593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b1dad722-9931-4435-a4a3-cfdecfa1fac8 · outbound

This paper cites On the blow-up profile of Keller–Segel–Patlak system.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations On the blow-up profile of Keller–Segel–Patlak system

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:31.215943Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c35fdcf2-22ab-4259-84c2-816699d2ec27 · outbound

This paper cites Carrillo, and Philippe Lauren¸ cot.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Carrillo, and Philippe Lauren¸ cot

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:31.197146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 159a7314-27bf-4ef3-9f56-328d45936c70 · outbound

This paper cites Carrillo, and Nader Masmoudi.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Carrillo, and Nader Masmoudi

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-16T00:24:30.158312Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a2a4cb92-0883-400e-afe5-c1c1bd1954a5 · outbound

This paper cites an unresolved cited work.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:24:31.177326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation edb6095c-72d3-4df3-8955-d01a99e02f56 · outbound

This paper cites Bouchut and B.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Bouchut and B

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:31.161111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1d6cda33-f4b0-45c6-9ac3-adf6db80be9f · outbound

This paper cites Existence of smooth solutions to coupled chemotaxis-fluid equations.Discrete and Continuous Dynamical Systems, 33(6):2271–2297, December 2012.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Existence of smooth solutions to coupled chemotaxis-fluid equations.Discrete and Continuous Dynamical Systems, 33(6):2271–2297, December 2012

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:31.139283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 943f9cf0-6875-49f6-b4cb-0dc6130a6889 · outbound

This paper cites Uniqueness and Long Time Asymp- totic for the Keller–Segel Equation: The Parabolic–Elliptic Case.Archive for Rational Mechanics and Analysis, 220(3):1159–1194, June 2016.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Uniqueness and Long Time Asymp- totic for the Keller–Segel Equation: The Parabolic–Elliptic Case.Archive for Rational Mechanics and Analysis, 220(3):1159–1194, June 2016

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:31.120376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 771708d4-205a-4caf-aed6-a6bc180e3e2b · outbound

This paper cites On convergence to equilibria for the Keller–Segel chemotaxis model.Journal of Differential Equations, 236(2):551– 569, May 2007.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations On convergence to equilibria for the Keller–Segel chemotaxis model.Journal of Differential Equations, 236(2):551– 569, May 2007

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:31.101956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f449a6cd-29e0-44df-9734-b6ad84a5af4a · outbound

This paper cites Strong so- lutions to the Keller-Segel-Navier-Stokes system in bounded Lipschitz domains, May.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Strong so- lutions to the Keller-Segel-Navier-Stokes system in bounded Lipschitz domains, May

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:31.085567Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5f969949-3da3-4765-9df9-2cfb5e9b6b1f · outbound

This paper cites Hillen and K.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Hillen and K

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:31.068142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fb136296-40e6-4a1e-b775-d1818dbd771b · outbound

This paper cites Nieders¨ achsische Staats- und Universit¨ atsbibliothek, 2003.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Nieders¨ achsische Staats- und Universit¨ atsbibliothek, 2003

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:31.047442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cc2008d2-fd74-455a-af65-e1274b668464 · outbound

This paper cites Long-time dynamics of classical Keller–Segel equation.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Long-time dynamics of classical Keller–Segel equation

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:31.027706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 36b45864-720a-4802-9f31-cfc0152a57f1 · outbound

This paper cites Keller and Lee A.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Keller and Lee A

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:31.009523Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b9df778e-8c50-4977-996d-3b25a2fdecaa · outbound

This paper cites Existence and uniqueness theorem on weak solutions to the parabolic–elliptic Keller–Segel system.Journal of Differential Equations, 253(7):2295–2313, October 2012.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Existence and uniqueness theorem on weak solutions to the parabolic–elliptic Keller–Segel system.Journal of Differential Equations, 253(7):2295–2313, October 2012

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:30.986128Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9b984767-323a-42b5-bb7b-f6de28668f23 · outbound

This paper cites an unresolved cited work.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:24:30.964554Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation bf6f283e-b61a-4e4a-b64c-15ac00f1d1f5 · outbound

This paper cites Threshold for shock formation in the hyperbolic Keller–Segel model.Applied Mathematics Letters, 50:56–63, December 2015.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Threshold for shock formation in the hyperbolic Keller–Segel model.Applied Mathematics Letters, 50:56–63, December 2015

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:30.935796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 132185c4-3686-4abd-a45b-e2f14c91e7a2 · outbound

This paper cites Finite time blowup for Keller-Segel equation with logistic damping in three dimensions.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Finite time blowup for Keller-Segel equation with logistic damping in three dimensions

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-16T00:24:30.247613Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a093c4e0-3960-4a87-a9b7-9c67d8cb39e0 · outbound

This paper cites Large friction limit of the almost pressureless Euler-Poisson system, March.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Large friction limit of the almost pressureless Euler-Poisson system, March

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:30.909552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ecd6f5ff-f7fd-4f59-a760-92c07aadd06b · outbound

This paper cites Global well-posedness, blow- up phenomenon and ill-posedness for the hyperbolic Keller-Segel equations.Journal of Differential Equations, 413:828–850, December 2024.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Global well-posedness, blow- up phenomenon and ill-posedness for the hyperbolic Keller-Segel equations.Journal of Differential Equations, 413:828–850, December 2024

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:30.887611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 294894c1-3bf6-4042-9788-0d96acfb9b96 · outbound

This paper cites Finite-time blow-up in hyperbolic Keller–Segel system of consumption type with logarithmic sensitivity.Nonlinearity, 37(4):045003, February 2024.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Finite-time blow-up in hyperbolic Keller–Segel system of consumption type with logarithmic sensitivity.Nonlinearity, 37(4):045003, February 2024

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:30.868600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d04238a6-4e56-407b-b073-8e74e0858436 · outbound

This paper cites Global well-posedness for a two-dimensional Keller-Segel-Euler system of consumption type.Journal of Differential Equations, 388:188–214, April 2024.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Global well-posedness for a two-dimensional Keller-Segel-Euler system of consumption type.Journal of Differential Equations, 388:188–214, April 2024

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:30.851449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a8df91f2-c305-45fd-932d-ec421dd40380 · outbound

This paper cites an unresolved cited work.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:24:30.829435Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 375b52f1-4819-41f9-bf21-5f07893577a6 · outbound

This paper cites Existence of Solutions of the Hyperbolic Keller-Segel Model.Transactions of the American Mathematical Society, 361(5):2319– 2335, 2009.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Existence of Solutions of the Hyperbolic Keller-Segel Model.Transactions of the American Mathematical Society, 361(5):2319– 2335, 2009

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:30.806209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2f104222-e835-4433-a571-a469ccf9aafc · outbound

This paper cites Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions$${n\geq 3}$$.Communications in Mathematical Physics, 367(2):665–681, April 2019.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions$${n\geq 3}$$.Communications in Mathematical Physics, 367(2):665–681, April 2019

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:30.785740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a5537681-6eda-4e6a-8194-76d679f65cf7 · outbound

This paper cites an unresolved cited work.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:24:30.768307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b8571445-d0b8-42ae-894f-4e0e05ab690d · outbound

This paper cites Application of the best constant of the Sobolev inequality to degen- erate Keller-Segel models.Advances in Differential Equations, 12(2):121–144, January 2007.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Application of the best constant of the Sobolev inequality to degen- erate Keller-Segel models.Advances in Differential Equations, 12(2):121–144, January 2007

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:30.747732Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 509707c6-8612-4b03-9ddd-a3708458cb33 · outbound

This paper cites Time periodic strong solutions to the Keller-Segel sys- tem coupled to Navier-Stokes equation.Journal of Differential Equations, 298:95–131, October 2021.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Time periodic strong solutions to the Keller-Segel sys- tem coupled to Navier-Stokes equation.Journal of Differential Equations, 298:95–131, October 2021

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:30.729011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4f8fc67f-97bc-4e6b-8baa-5d4e229e8c52 · outbound

This paper cites an unresolved cited work.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-16T00:24:30.325921Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 84b06472-5ca1-46d0-a97d-7ffc3b570812 · outbound

This paper cites Stabilization in a two-dimensional chemotaxis-Navier–Stokes system.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Stabilization in a two-dimensional chemotaxis-Navier–Stokes system

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:24:30.707570Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 76426090-3fa3-483e-b750-f2ce94a65ca1 · outbound

This paper cites Strong solutions to the Keller-Segel-Navier-Stokes system in bounded Lipschitz domains.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Strong solutions to the Keller-Segel-Navier-Stokes system in bounded Lipschitz domains

Reference 2025

Resolution: verified exact; local_arxiv, observed 2026-08-16T00:24:30.661343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2af0d39e-b66d-40b2-b1fa-940d435bb9af · outbound

This paper cites an unresolved cited work.

The traveling wave solutions of the 1D hyperbolic Keller-Segel equations Unresolved cited work

Reference 2026

Resolution: verified exact; raw_fallback, observed 2026-08-16T00:24:30.603202Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

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