On a Class of Stochastic Damped Wave Equation

Authors

Hatice Taskesen Department of Mathematics, Faculty of Science, Van Yuzuncu Yil University, Van, Turkey https://orcid.org/0000-0003-1058-0507
Beytullah Ya˘gız Department of Statistics, Institute of Science, Van Yuzuncu Yil University, Van, Turkey https://orcid.org/0000-0001-5453-185X

https://doi.org/10.61383/ejam.20242146

Keywords:

Stochastic wave equation, mild solution, blow up

Abstract

The present work considers a wave equation with multiplicative Gaussian white noise and weak dissipative term on a bounded domain. We first give a theorem including the local existence of mild solutions. An energy bound and a differential inequality are used to give sufficient conditions that provide the blow-up of mild local solutions of the stochastic wave equation. The paper's main contribution comes from handling a multiplicative noise and a general source term contrary to the articles that exist in the literature.

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