Paper Citation Record · LEDGER

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III

As of 21 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2507.08274.

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

pith.paper-citation-record.v1
2507.08274 v2

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:35:10.228510Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

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 exact0
verified fuzzy22
unresolved8
parse uncertain0
malformed identifier0
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 57ed109b-4902-4566-830c-2d69772fabcf · outbound

This paper cites D’Abbicco, Small data solutions for the Euler-Poisson-Darboux equation with a power non- linearity.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III D’Abbicco, Small data solutions for the Euler-Poisson-Darboux equation with a power non- linearity

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.950623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 85fb2ebf-b2a1-4c02-b66b-4eb1b7813aa7 · outbound

This paper cites D’Abbicco, The threshold of effective damping for semilinear wave equations.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III D’Abbicco, The threshold of effective damping for semilinear wave equations

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.939428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation bdbc6f42-0c9f-47f2-aa28-611f4b9d1ee4 · outbound

This paper cites D’Abbicco, S.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III D’Abbicco, S

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.929056Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8858b66a-67a9-4bf0-9083-06cd689c9269 · outbound

This paper cites Alinhac, The null condition for quasilinear wave equations in two space dimensions I.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Alinhac, The null condition for quasilinear wave equations in two space dimensions I

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T18:35:07.649181Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1579380f-2a2e-4d68-a9c7-b2d3b842d3f4 · outbound

This paper cites Alinhac, The null condition for quasilinear wave equations in two space dimensions, II.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Alinhac, The null condition for quasilinear wave equations in two space dimensions, II

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.911044Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 943e9f48-b790-4cab-bc10-8892e54f5617 · outbound

This paper cites Alinhac, An example of blowup at infinity for a quasilinear wave equations.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Alinhac, An example of blowup at infinity for a quasilinear wave equations

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.901741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7ebe684e-3dbc-49aa-b1c5-3a79d001b579 · outbound

This paper cites an unresolved cited work.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:35:10.892181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 94dfbf5c-27ce-45c6-b45a-b62d9729f5c2 · outbound

This paper cites an unresolved cited work.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:35:10.882630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d61bfb64-8c1d-4a5d-8dee-e200f94c0290 · outbound

This paper cites Fujita, On the blowing up of solutions of the Cauchy Problem for ut = ∆u + u1+α.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Fujita, On the blowing up of solutions of the Cauchy Problem for ut = ∆u + u1+α

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.872733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b3d163b7-0401-43ac-833e-39f7be3d9cc9 · outbound

This paper cites Morawetz type estimate for damped wave equation in $\mathbb{R}^n (n\geq 4)$ and its application.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Morawetz type estimate for damped wave equation in $\mathbb{R}^n (n\geq 4)$ and its application

Reference 10

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T18:35:10.660375Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation caa4d2e1-7a8c-4d2e-a8f5-01dd1a2c3ebb · outbound

This paper cites Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, II.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, II

Reference 11

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T18:35:10.481131Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation c47d68f0-009d-4ae6-a5cc-1cdc8fb7e6dc · outbound

This paper cites Preprint (2025).

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Preprint (2025)

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.860181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7501e955-c57a-4bf3-a288-d691daf99253 · outbound

This paper cites H ¨ormander, Lectures on nonlinear hyperbolic equations.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III H ¨ormander, Lectures on nonlinear hyperbolic equations

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.850789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2efc5884-124e-497e-b5f0-20eb9195cf2d · outbound

This paper cites Ikeda, M.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Ikeda, M

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.840517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation c801efe2-f563-41fe-ae4a-4b4b54a8f1aa · outbound

This paper cites an unresolved cited work.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:35:10.830234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8c78d722-3e09-4131-ab7f-63cdff07c14d · outbound

This paper cites Klainerman, Uniform decay estimates and Lorentz invariance of the classical wave equation.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Klainerman, Uniform decay estimates and Lorentz invariance of the classical wave equation

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.819925Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7da7105b-795b-4dfd-b0eb-b1385c229b91 · outbound

This paper cites Klainerman, G.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Klainerman, G

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T18:35:08.464894Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e9144965-c0a6-417d-9650-9719941f10b5 · outbound

This paper cites Takamura, K.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Takamura, K

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.802815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e5623b37-d637-4adb-9ffd-305ea1ff7e27 · outbound

This paper cites Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, I.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, I

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T18:35:08.624866Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e047762-1963-43d1-8192-323c938a644e · outbound

This paper cites an unresolved cited work.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T18:35:08.666619Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b9a3c3e9-5664-4b3d-ad5e-34527b850c30 · outbound

This paper cites an unresolved cited work.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:35:10.787545Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 18d7203f-f0f0-452e-8f57-04c54c3526f2 · outbound

This paper cites Lindblad, On the lifespan of solutions of nonlinear wave equations with small initial data.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Lindblad, On the lifespan of solutions of nonlinear wave equations with small initial data

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.778711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9f5be8eb-eac2-4947-a1ad-e654a5dd96f1 · outbound

This paper cites Lindblad, Global solutions of quasilinear wave equations.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Lindblad, Global solutions of quasilinear wave equations

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.769167Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 99ea69be-adb0-4761-9035-6654f31adcdc · outbound

This paper cites Olver, D.W.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Olver, D.W

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.759243Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7365b0db-73ff-4453-878c-358b2c8bd6c5 · outbound

This paper cites Palmieri, On the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equa- tion with power nonlinearity.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Palmieri, On the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equa- tion with power nonlinearity

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.749430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7788326b-eeb7-464d-ad8e-59e874c1dbc7 · outbound

This paper cites Palmieri, M.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Palmieri, M

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.739494Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7a07fa19-f192-4719-85f2-a102fa86c1e4 · outbound

This paper cites Palmieri, Tu Ziheng, A blow-up result for a semilinear wave equation with scale-invariant damping andmass and nonlinearity of derivative type.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Palmieri, Tu Ziheng, A blow-up result for a semilinear wave equation with scale-invariant damping andmass and nonlinearity of derivative type

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.728775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation c2ffb2b6-094e-4d30-9048-8f89cfacf170 · outbound

This paper cites Strauss, Nonlinear scattering theory at low energy.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Strauss, Nonlinear scattering theory at low energy

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.717627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 156b5700-0a20-4249-8e19-03e753242150 · outbound

This paper cites Differential Integral Equations 32 (2019), no.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Differential Integral Equations 32 (2019), no

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.705400Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 38ae83aa-a6f6-4db1-9dd2-fff59c495004 · outbound

This paper cites Wakasugi, Critical exponent for the semilinear wave equation with scale invariant damping, in: Fourier Analysis.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Wakasugi, Critical exponent for the semilinear wave equation with scale invariant damping, in: Fourier Analysis

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.691908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation de437692-a17b-481c-ae70-960f26eaeecd · outbound

This paper cites Watson, A treatise on the theory of Bessel functions.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Watson, A treatise on the theory of Bessel functions

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.681513Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f7b7091e-171b-4cee-9eb2-2855b155334d · outbound

This paper cites Wirth, Solution representations for a wave equation with weak dissipation.

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III Wirth, Solution representations for a wave equation with weak dissipation

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:10.671350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

No inbound Pith citation observations are available.