Paper Citation Record · LEDGER

Collapsing-tube type II blow-up for the energy-supercritical heat equation

As of 20 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2607.16733.

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

pith.paper-citation-record.v1
2607.16733 v1

Coverage vector

measured 37 of 37 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-01T20:11:06.101610Z

measured 37 of 37 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

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Reference resolution

37 of 37 outbound references displayed

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Outbound references

Observation ee230b61-0310-4059-b641-52ae5ed70648 · outbound

This paper cites an unresolved cited work.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:02.466337Z

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Unavailable: canonical work link unavailable.

Observation d3ac3089-49b4-48e3-a4c2-1767ea26fc92 · outbound

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

Collapsing-tube type II blow-up for the energy-supercritical heat equation Existence of finite time blow-up in Keller- Segel system.Ann

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:02.590880Z

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Observation a988a57b-925c-474f-be97-0675d5a06339 · outbound

This paper cites Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system.J.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system.J

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:02.822996Z

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Observation a2d9bb00-3d9c-4ec0-90a7-2bc178f29b01 · outbound

This paper cites Remark on Luo-Hou’s ansatz for a self-similar solution to the 3D Euler equations.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Remark on Luo-Hou’s ansatz for a self-similar solution to the 3D Euler equations

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:02.979593Z

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Observation f9d625c2-480f-475f-8455-956980ca02fe · outbound

This paper cites Nonradial type II blow up for the energy-supercritical semilinear heat equation.Anal.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Nonradial type II blow up for the energy-supercritical semilinear heat equation.Anal

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:03.112542Z

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Observation 84d1a524-2d07-4dac-a7ef-87bd09dedc43 · outbound

This paper cites Refined description and stability for singular solutions of the 2D Keller-Segel system.Comm.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Refined description and stability for singular solutions of the 2D Keller-Segel system.Comm

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:03.312816Z

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Observation 0d670d5a-0788-4253-869b-91675d51ca96 · outbound

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

Collapsing-tube type II blow-up for the energy-supercritical heat equation Collapsing-ring blowup solutions for the Keller-Segel system in three dimensions and higher.J

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:03.442806Z

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Observation faca4dd2-3274-4d8c-ad90-e57d7130f3bc · outbound

This paper cites Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions.Comm.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions.Comm

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:03.622043Z

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Observation ba38d80b-9d9b-46a2-ab9e-41c46339e577 · outbound

This paper cites Strongly anisotropic type II blow up at an isolated point.J.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Strongly anisotropic type II blow up at an isolated point.J

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:03.794204Z

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Observation 2e68b487-4fc8-4144-a22f-540a9f4f6fcf · outbound

This paper cites Green’s function and infinite-time bubbling in the critical nonlinear heat equation.J.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Green’s function and infinite-time bubbling in the critical nonlinear heat equation.J

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:03.922458Z

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Observation 12267596-af89-4868-a84a-6f06938efde5 · outbound

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

Collapsing-tube type II blow-up for the energy-supercritical heat equation Existence and stability of infinite time blow-up in the Keller-Segel system.Arch

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:04.051774Z

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Observation 6e9727a3-d71d-4ef9-a592-ccee7d7bcc28 · outbound

This paper cites Singularity formation for the two-dimensional harmonic map flow intoS 2.Invent.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Singularity formation for the two-dimensional harmonic map flow intoS 2.Invent

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:04.131539Z

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Observation e0e6d34d-c98b-4f52-a6f9-0b9e973f273e · outbound

This paper cites Type II Blow-up in the 5-dimensional Energy Critical Heat Equation.Acta Math.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Type II Blow-up in the 5-dimensional Energy Critical Heat Equation.Acta Math

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:04.197123Z

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Observation 8db9359c-f981-41ea-8383-dbd9952bf118 · outbound

This paper cites Geometry driven type II higher dimensional blow-up for the critical heat equation.J.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Geometry driven type II higher dimensional blow-up for the critical heat equation.J

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:04.289390Z

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Observation 21853829-d695-4b23-b349-3cc6ba73399d · outbound

This paper cites Type II finite time blow-up for the energy critical heat equation inR 4.Discrete Contin.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Type II finite time blow-up for the energy critical heat equation inR 4.Discrete Contin

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:04.366167Z

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Observation c8ebac78-1398-437a-aecf-251bd067ace8 · outbound

This paper cites Herrero, and Juan J.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Herrero, and Juan J

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:04.446543Z

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Observation d646a2d4-70bb-458e-9f87-20cac0a4f395 · outbound

This paper cites On the blowing up of solutions of the Cauchy problem foru t = ∆u+u 1+α.J.

Collapsing-tube type II blow-up for the energy-supercritical heat equation On the blowing up of solutions of the Cauchy problem foru t = ∆u+u 1+α.J

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:04.542167Z

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Observation 881fcc2c-21e3-4f52-8cf3-2794da704f56 · outbound

This paper cites an unresolved cited work.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:04.646586Z

Source-reported events for the cited work

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Observation dfcd90df-95be-4e41-bbed-f7e5364b6459 · outbound

This paper cites Blow up rate for semilinear heat equations with subcritical nonlinearity.Indiana Univ.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Blow up rate for semilinear heat equations with subcritical nonlinearity.Indiana Univ

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:04.706151Z

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Observation 8878713d-dc63-46f3-abee-75931b9bd4a6 · outbound

This paper cites On blow-up rate for sign-changing solutions in a convex domain.Math.

Collapsing-tube type II blow-up for the energy-supercritical heat equation On blow-up rate for sign-changing solutions in a convex domain.Math

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:04.775568Z

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Observation 428d7ff2-8b63-4f34-9d1c-b6f8c9a8776e · outbound

This paper cites A type II blowup for the six dimensional energy critical heat equation.Ann.

Collapsing-tube type II blow-up for the energy-supercritical heat equation A type II blowup for the six dimensional energy critical heat equation.Ann

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:04.848266Z

Source-reported events for the cited work

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Observation 2c1294af-49e6-469e-b110-c23d015f1e3d · outbound

This paper cites Herrero and Juan J.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Herrero and Juan J

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:04.915178Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 85b8f401-5a1e-40b3-a010-550ae7224d66 · outbound

This paper cites A blow up result for semilinear heat equations in the supercritical case.

Collapsing-tube type II blow-up for the energy-supercritical heat equation A blow up result for semilinear heat equations in the supercritical case

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:04.980198Z

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Observation bc1bb2d7-3019-4dcf-9140-e493a6b4976b · outbound

This paper cites Hou and De Huang.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Hou and De Huang

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:05.058711Z

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Observation 0d273138-3f29-48e6-9673-07d8f2ad41f3 · outbound

This paper cites Nearly self-similar blowup of generalized axisymmetric Navier-Stokes equations.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Nearly self-similar blowup of generalized axisymmetric Navier-Stokes equations

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:05.115140Z

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Observation 8817e62c-70b8-4200-bdc4-e13cc5117116 · outbound

This paper cites On classification of global dynamics for energy-critical equivariant harmonic map heat flows and radial nonlinear heat equation.Comm.

Collapsing-tube type II blow-up for the energy-supercritical heat equation On classification of global dynamics for energy-critical equivariant harmonic map heat flows and radial nonlinear heat equation.Comm

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:05.177510Z

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Observation c1b4099d-6ffb-4fd4-8b65-91a379af63b5 · outbound

This paper cites On nonexistence of type II blowup for a supercritical nonlinear heat equation.

Collapsing-tube type II blow-up for the energy-supercritical heat equation On nonexistence of type II blowup for a supercritical nonlinear heat equation

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:05.254073Z

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Observation ca65a31f-4853-42ee-aaa2-10f4afbf4fb4 · outbound

This paper cites Classification of type I and type II behaviors for a supercritical nonlinear heat equation.J.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Classification of type I and type II behaviors for a supercritical nonlinear heat equation.J

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:05.303483Z

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Observation 6dc62031-8e55-4474-a65c-afeed26cb041 · outbound

This paper cites Stability of the blow-up profile for equations of the typeu t = ∆u+|u| p−1u.Duke Math.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Stability of the blow-up profile for equations of the typeu t = ∆u+|u| p−1u.Duke Math

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:05.344522Z

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Observation 674c9f03-575c-42ab-b298-e50af3a0df84 · outbound

This paper cites Boundedness of global solutions for a supercritical semilinear heat equation and its application.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Boundedness of global solutions for a supercritical semilinear heat equation and its application

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:05.422755Z

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Unavailable: canonical work link unavailable.

Observation 6e7f52a5-0108-4709-ba7d-7933ea12d1c0 · outbound

This paper cites Nonexistence of type II blowup solution for a semilinear heat equation.J.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Nonexistence of type II blowup solution for a semilinear heat equation.J

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:05.544845Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2806a4eb-0ff6-4f80-b190-59e9755c298c · outbound

This paper cites Bubbling blow-up in critical elliptic and parabolic problems.Notices Amer.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Bubbling blow-up in critical elliptic and parabolic problems.Notices Amer

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:05.618158Z

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Observation 52155d50-f326-4f78-80a3-01d913cf5437 · outbound

This paper cites Optimal Liouville theorems for superlinear parabolic problems.Duke Math.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Optimal Liouville theorems for superlinear parabolic problems.Duke Math

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:05.719645Z

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Observation d519a218-ca83-469c-85c9-336c9fc8e3cb · outbound

This paper cites Birkh¨ auser Advanced Texts: Basler Lehrb¨ ucher.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Birkh¨ auser Advanced Texts: Basler Lehrb¨ ucher

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:05.830876Z

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Observation 1c4962f3-cef5-46e5-9c6a-60d5a5b3b406 · outbound

This paper cites Type II blow-up for the four dimensional energy critical semi linear heat equation.J.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Type II blow-up for the four dimensional energy critical semi linear heat equation.J

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:05.907464Z

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Observation 1c2fd829-ddaa-4c5a-a15a-344d3b342bd8 · outbound

This paper cites Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation.Ann.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation.Ann

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:06.011523Z

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Observation 4d63a963-7ac1-42a5-a9d0-7e76d8107e20 · outbound

This paper cites Refined blowup analysis and nonexistence of Type II blowups for an energy critical nonlinear heat equation.

Collapsing-tube type II blow-up for the energy-supercritical heat equation Refined blowup analysis and nonexistence of Type II blowups for an energy critical nonlinear heat equation

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-01T20:11:06.101610Z

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