Nonlinear stochastic wave and heat equations

We study nonlinear wave and heat equations on ℝd driven by a spatially homogeneous Wiener process. For the wave equation we consider the cases of d = 1, 2, 3. The heat equation is considered on an arbitrary ℝd-space. We give necessary and sufficient conditions for the existence of a function-valued...

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Bibliographic Details
Published in:Probability theory and related fields 2000-03, Vol.116 (3), p.421-443
Main Authors: PESZAT, S, ZABCZYK, J
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical analysis
Mathematics
Partial differential equations
Probability
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Stochastic analysis
Stochastic processes
Thermodynamics
Wave equations
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Summary:We study nonlinear wave and heat equations on ℝd driven by a spatially homogeneous Wiener process. For the wave equation we consider the cases of d = 1, 2, 3. The heat equation is considered on an arbitrary ℝd-space. We give necessary and sufficient conditions for the existence of a function-valued solution in terms of the covariance kernel of the noise.
ISSN:0178-8051
1432-2064
DOI:10.1007/s004400050257