Non-existence results for stochastic wave equations in one dimension

Foondun, Mohammud; Nualart, Eulàlia

doi:http://dx.doi.org/10.1016/j.jde.2022.02.038

Non-existence results for stochastic wave equations in one dimension

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Foondun M, Nualart E. Non-existence results for stochastic wave equations in one dimension. J Differ Equ. 2022;318:557-78. DOI: 10.1016/j.jde.2022.02.038

Abstract

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 [...] where Ẇ 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 [...] is studied in relation to non-existence of global solutions.