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arXiv · 1910.05981

Blow-up of solutions to semilinear strongly damped wave equations with different nonlinear terms in an exterior domain

Wenhui Chen·Ahmad Z. Fino
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Abstract

In this paper, we consider the initial boundary value problem in an exterior domain for semilinear strongly damped wave equations with power nonlinear term of the derivative-type $|u_t|^q$ or the mixed-type $|u|^p+|u_t|^q$, where $p,q>1$. On one hand, employing the Banach fixed-point theorem we prove local (in time) existence of mild solutions. On the other hand, under some conditions for initial data and the exponents of power nonlinear terms, the blow-up results are derived by applying the test function method.

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Wenhui Chen, Ahmad Z. Fino. 2019-10-14. Blow-up of solutions to semilinear strongly damped wave equations with different nonlinear terms in an exterior domain. https://doi.org/10.1002/mma.7223

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