Blow-up for Strauss type wave equation with damping and potential

We study a kind of nonlinear wave equations with damping and potential, whose coefficients are both critical in the sense of the scaling and depend only on the spatial variables. Based on the earlier works, one may think there are two kinds of blow-up phenomenons when the exponent of the nonlinear t...

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Bibliographic Details
Published in:arXiv.org 2020-10
Main Authors: Dai, Wei, Kubo, Hideo, Sobajima, Motohiro
Format: Article
Language:English
Subjects:
Damping
Nonlinear equations
Upper bounds
Wave equations
Online Access:Get full text
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Summary:We study a kind of nonlinear wave equations with damping and potential, whose coefficients are both critical in the sense of the scaling and depend only on the spatial variables. Based on the earlier works, one may think there are two kinds of blow-up phenomenons when the exponent of the nonlinear term is small. It also means there are two kinds of law to determine the critical exponent. In this paper, we obtain a blow-up result and get the estimate of the upper bound of the lifespan in critical and sub-critical cases. All of the results support such a conjecture, although for now, the existence part is still open.
ISSN:2331-8422
DOI:10.48550/arxiv.1909.08885