Non-existence results for stochastic wave equations in one dimension

Authors: Mohammud Foondun and Eulàlia Nualart

Journal of Differential Equations, Vol. 318, 557 - 578, May, 2022

The purpose of this paper is to extend recent results of [2] and [10] for the stochastic heat equation to the stochastic wave equation given by [Formula presented] where W˙ is space-time white noise, σ is a real-valued globally Lipschitz function but b is assumed to be only locally Lipschitz continuous. Three types of domain conditions are studied: D=[0,1] with homogeneous Dirichlet boundary conditions, D=[0,2π] with periodic boundary conditions, and D=R. Then, under suitable conditions, the following integrability condition [Formula presented] is studied in relation to non-existence of global solutions.