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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arXiv · 2610.25668

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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Ikeda Masahiro, Tu Ziheng, Wang Chengbo. 2026-10-19. Blow-up of damped semilinear wave equation with short range potential and critical power nonlinearity. https://arxiv.org/abs/2610.25668

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