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arXiv · 1104.3279

Stochastic Wave Equations with Nonlinear Damping and Source Terms

Hongjun Gao·Boling Guo·Fei Liang
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Abstract

In this paper, we discuss an initial boundary value problem for the stochastic wave equation involving the nonlinear damping term $|u_t|^{q-2}u_t$ and a source term of the type $|u|^{p-2}u$. We firstly establish the local existence and uniqueness of solution by the Galerkin approximation method and show that the solution is global for $q\geq p$. Secondly, by an appropriate energy inequality, the local solution of the stochastic equations will blow up with positive probability or explosive in energy sense for $p>q$.

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Hongjun Gao, Boling Guo, Fei Liang. 2011-04-17. Stochastic Wave Equations with Nonlinear Damping and Source Terms. https://arxiv.org/abs/1104.3279

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