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arXiv · 1807.06164

On the blow-up for critical semilinear wave equations with damping in the scattering case

Kyouhei Wakasa·Borislav Yordanov
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Abstract

We consider the Cauchy problem for semilinear wave equations with variable coefficients and time-dependent scattering damping in $\mathbf{R}^n$, where $n\geq 2$. It is expected that the critical exponent will be Strauss' number $p_0(n)$, which is also the one for semilinear wave equations without damping terms. Lai and Takamura (2018) have obtained the blow-up part, together with the upper bound of lifespan, in the sub-critical case $p<p_0(n)$. In this paper, we extend their results to the critical case $p=p_0(n)$. The proof is based on Wakasa and Yordanov (2018), which concerns the blow-up and upper bound of lifespan for critical semilinear wave equations with variable coefficients.

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Kyouhei Wakasa, Borislav Yordanov. 2018-07-17. On the blow-up for critical semilinear wave equations with damping in the scattering case. https://arxiv.org/abs/1807.06164

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