Stochastic wave equations with nonlinear damping and source terms (Q2842033)
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scientific article; zbMATH DE number 6192887
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stochastic wave equations with nonlinear damping and source terms |
scientific article; zbMATH DE number 6192887 |
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30 July 2013
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stochastic wave equation
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additive noise
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nonlinear damping
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explosion of solutions
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energy inequality
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Stochastic wave equations with nonlinear damping and source terms (English)
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The paper discusses existence und uniqueness of solutions of an initial boundary value problem for a stochastic wave equation with additive white noise on a bounded domain in \(\mathbb R^d\) with smooth boundary, with a nonlinear damping term \(|u_t|^{q-2}u_t\) and with a source term \(|u|^{p-2}u\). For the case \(q\geq p\) existence and uniqueness of solutions is established by using a Galerkin approximation. For the case \(p>q\) it is shown that local solutions blow up in the \(L^2\) norm with positive probability, or an associated energy goes to infinity, in finite time.
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