A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain

Ahmad Z. Fino; Wenhui Chen

doi:10.3934/cpaa.2020243

Article Contents

2020, Volume 19, Issue 12: 5387-5411. Doi: 10.3934/cpaa.2020243

This issue Previous Article Limiting behavior of non-autonomous stochastic reaction-diffusion equations with colored noise on unbounded thin domains Next Article Classification of solutions to a system of

$ n^{\rm th} $

order equations on

$ \mathbb R^n $

A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain

Ahmad Z. Fino^1, , and
Wenhui Chen^2,

1.
Department of Mathematics, Faculty of Sciences, Lebanese University, Tripoli, P.O. Box 1352, Lebanon
2.
Faculty of Mathematics and Computer Science, Technical University Bergakademie Freiberg, Freiberg, 09596, Germany

^* Corresponding author
^* Corresponding author

Received: April 2020

Revised: July 2020

Early access: September 2020

Published: December 2020

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Abstract

We study two-dimensional semilinear strongly damped wave equation with mixed nonlinearity $ |u|^p+|u_t|^q $ in an exterior domain, where $ p, q>1 $. We prove global (in time) existence of small data solution with suitable higher regularity by using a weighted energy method, and assuming some conditions on powers of nonlinearity.

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Mathematics Subject Classification: Primary: 35A01; Secondary: 35L20, 35L05.

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