Existence of invariant manifolds for coupled parabolic and hyperbolic stochastic partial differential equations
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 exponent...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2005 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/23664 |
| Acceso en línea: | http://hdl.handle.net/11441/23664 https://doi.org/10.1088/0951-7715/18/2/015 |
| Access Level: | acceso abierto |
| Palabra clave: | Invariant manifolds paraboliic stochastic partial differential equations hyperbolic stochastic partial differential equations |
| Sumario: | 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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