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

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

2009-12-09

arxiv.org/abs/0912.1735v1

Annals of Applied Probability 2009, Vol. 19, No. 6, 2039-2046

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP602 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP602

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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