Nonlinear stochastic wave and heat equations

Authors
Peszat, S Zabczyk, J
Citation
S. Peszat et J. Zabczyk, Nonlinear stochastic wave and heat equations, PROB TH REL, 116(3), 2000, pp. 421-443
Citations number
20
Categorie Soggetti
Mathematics
Journal title
PROBABILITY THEORY AND RELATED FIELDS
ISSN journal
01788051 → ACNP
Volume
116
Issue
3
Year of publication
2000
Pages
421 - 443
Database
ISI
SICI code
0178-8051(200003)116:3<421:NSWAHE>2.0.ZU;2-J
Abstract
We study nonlinear wave and heat equations on R-d driven by a spatially hom ogeneous Wiener process. For the wave equation we consider the cases of d = 1, 2, 3. The heat equation is considered on an arbitrary R-d-space. We giv e necessary and sufficient conditions for the existence of a function-value d solution in terms of the covariance kernel of the noise.