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Sharp lifespan estimates for Nakao's problem in one space dimension

  • Wenhui Chen
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Abstract

In this paper, we consider Nakao's problem in one space dimension, which couples a semilinear damped wave equation with a semilinear wave equation. For compactly supported energy data satisfying suitable integral sign conditions, we establish sharp lifespan estimates for all powers p,q>1. The estimates are classified according to whether the total integral of the initial speed in the wave equation is positive or zero.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026sharp,
  title = {{Sharp lifespan estimates for Nakao's problem in one space dimension}},
  author = {Wenhui Chen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.14736},
  eprint = {2607.14736},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.14736},
}
RIS
TY  - UNPB
TI  - Sharp lifespan estimates for Nakao's problem in one space dimension
AU  - Wenhui Chen
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2607.14736
UR  - https://arxiv.org/abs/2607.14736
AB  - In this paper, we consider Nakao's problem in one space dimension, which couples a semilinear damped wave equation with a semilinear wave equation. For compactly supported energy data satisfying suitable integral sign conditions, we establish sharp lifespan estimates for all powers p,q>1. The estimates are classified according to whether the total integral of the initial speed in the wave equation is positive or zero.
ER  -