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arXiv · 0912.1735

Nonlinear stochastic wave equations: Blow-up of second moments in $L^2$-norm

Pao-Liu Chow
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Abstract

The paper is concerned with the problem of explosive solutions for a class of nonlinear stochastic wave equations in a domain $\mathcal{D}\subset\mathbb{R}^d$ for $d\leq3$. Under appropriate conditions on the initial data, the nonlinear term and the noise intensity is proved in Theorem 3.1 that the $L^2$-norm of the solution will blow up at a finite time in the mean-square sense. An example is given to show an application of the theorem.

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Pao-Liu Chow. 2009-12-09. Nonlinear stochastic wave equations: Blow-up of second moments in $L^2$-norm. https://doi.org/10.1214/09-aap602

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