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February 2002 Stochastic Wave Equations with Polynomial Nonlinearity
Pao-Liu Chow
Ann. Appl. Probab. 12(1): 361-381 (February 2002). DOI: 10.1214/aoap/1015961168

Abstract

This paper is concerned with a class of nonlinear stochastic wave equations in $\mathbb{R}^d$ with $d \leq 3$, for which the nonlinear terms are polynomial of degree $m$. As an example of the nonexistence of a global solution in general, it is shown that there exists an explosive solution of some cubically nonlinear wave equation with a noise term. Then the existence and uniqueness theorems for local and global solutions in Sobolev space $H_1$ are proven with the degree of polynomial $m \leq 3$ for $d = 3$, and $m \geq 2$ for $d = 1$ or 2.

Citation

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Pao-Liu Chow. "Stochastic Wave Equations with Polynomial Nonlinearity." Ann. Appl. Probab. 12 (1) 361 - 381, February 2002. https://doi.org/10.1214/aoap/1015961168

Information

Published: February 2002
First available in Project Euclid: 12 March 2002

zbMATH: 1017.60071
MathSciNet: MR1890069
Digital Object Identifier: 10.1214/aoap/1015961168

Subjects:
Primary: 60H15
Secondary: 60H05

Keywords: local and global solutions , polynomial nonlinearity , Stochastic wave equation

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.12 • No. 1 • February 2002
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