Article
Existence of invariant manifolds for coupled parabolic and hyperbolic stochastic partial differential equations
Author/s | Caraballo Garrido, Tomás
Chueshov, Igor D. Langa Rosado, José Antonio |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2005 |
Deposit Date | 2015-04-08 |
Published in |
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Abstract | An abstract system of coupled nonlinear parabolic-hyperbolic partial differential equations subjected to additive white noise is considered. The system models temperature dependent or heat generating wave phenomena in a ... An abstract system of coupled nonlinear parabolic-hyperbolic partial differential equations subjected to additive white noise is considered. The system models temperature dependent or heat generating wave phenomena in a continuum random medium. Under suitable conditions, the existence of an exponentially attracting random invariant manifold for the coupled system is proved, and as a consequence, the system can be reduced to a single stochastic hyperbolic equation with a modified nonlinear term. Finally it is also proved that this random manifold converges to its deterministic counterpart when the intensity of noise tends to zero. |
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