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PreprintCC BY 4.0arXiv

Blow-up of damped semilinear wave equation with short range potential and critical power nonlinearity

  • Ikeda Masahiro
  • Tu Ziheng
  • Wang Chengbo
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Abstract

The present paper is devoted to the study of a semilinear wave equation with spatially dependent scattering damping and a short-range potential, with particular focus on determining the critical exponent for the power-type nonlinearity. By employing the test function method, we establish wave-type blow-up results and derive lifespan estimates at the critical level. The main contribution of this work lies in providing a uniform asymptotic analysis for a family of test functions, which is achieved through a detailed investigation of a parametric second-order elliptic equation. As a further novelty, we relax the radial symmetry condition conventionally imposed on the coefficients D and V by resorting to the comparison principle in conjunction with a monotone exhaustion argument.

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Cite

BibTeXRIS
BibTeX
@misc{masahiro2026blowup,
  title = {{Blow-up of damped semilinear wave equation with short range potential and critical power nonlinearity}},
  author = {Ikeda Masahiro and Tu Ziheng and Wang Chengbo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25668},
  eprint = {2610.25668},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25668},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Blow-up of damped semilinear wave equation with short range potential and critical power nonlinearity
AU  - Ikeda Masahiro
AU  - Tu Ziheng
AU  - Wang Chengbo
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.25668
UR  - https://arxiv.org/abs/2610.25668
AB  - The present paper is devoted to the study of a semilinear wave equation with spatially dependent scattering damping and a short-range potential, with particular focus on determining the critical exponent for the power-type nonlinearity. By employing the test function method, we establish wave-type blow-up results and derive lifespan estimates at the critical level. The main contribution of this work lies in providing a uniform asymptotic analysis for a family of test functions, which is achieved through a detailed investigation of a parametric second-order elliptic equation. As a further novelty, we relax the radial symmetry condition conventionally imposed on the coefficients D and V by resorting to the comparison principle in conjunction with a monotone exhaustion argument.
ER  -