NONLINEAR STOCHASTIC WAVE EQUATIONS: BLOW-UP OF SECOND MOMENTS IN L²-NORM

The paper is concerned with the problem of explosive solutions for a class of nonlinear stochastic wave equations in a domain ${\cal D}\subset {\Bbb R}^{d}$ 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-no...

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Bibliographic Details
Published in:The Annals of applied probability 2009-12, Vol.19 (6), p.2039-2046
Main Author: Chow, Pao-Liu
Format: Article
Language:English
Subjects:
60H05
60H15
Applied mathematics
Covariance
energy equation
explosive solutions
Explosives
Information retrieval noise
local and global solutions
Mathematical functions
Mathematical theorems
Nonlinear
Polynomials
stochastic wave equations
Wave equations
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Summary:The paper is concerned with the problem of explosive solutions for a class of nonlinear stochastic wave equations in a domain ${\cal D}\subset {\Bbb R}^{d}$ 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.
ISSN:1050-5164
2168-8737
DOI:10.1214/09-aap602