Non-existence results for stochastic wave equations in one dimension

TL;DR

This paper extends non-existence results for stochastic wave equations in one dimension by establishing integrability conditions that prevent global solutions, advancing understanding of solution behavior in stochastic PDEs.

Contribution

It introduces a new integrability criterion for non-existence of solutions, extending prior work to stochastic wave equations in one dimension.

Findings

Derives a specific integrability condition for non-existence

Extends previous results from stochastic heat equations to wave equations

Provides theoretical framework for solution non-existence

Abstract

The purpose of this paper is extend recent results of Bonder-Groisman and Foondun-Nualart to the stochastic wave equation. In particular, a suitable integrability condition for non-existence of global solutions is derived.