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.
Publié le : 2009-12-15
Classification:
Nonlinear,
stochastic wave equations,
local and global solutions,
explosive solutions,
energy equation,
60H15,
60H05
@article{1259158765,
author = {Chow, Pao-Liu},
title = {Nonlinear stochastic wave equations: Blow-up of second moments in L<sup>2</sup>-norm},
journal = {Ann. Appl. Probab.},
volume = {19},
number = {1},
year = {2009},
pages = { 2039-2046},
language = {en},
url = {http://dml.mathdoc.fr/item/1259158765}
}
Chow, Pao-Liu. Nonlinear stochastic wave equations: Blow-up of second moments in L2-norm. Ann. Appl. Probab., Tome 19 (2009) no. 1, pp. 2039-2046. http://gdmltest.u-ga.fr/item/1259158765/