Nonlinear stochastic wave equations: Blow-up of second moments in L2-norm

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≤3. Under appropriate conditions on the initial data, the nonlinear term and the noise intensity is proved in Theorem 3.1 that the L²-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.