Article
Stabilisation of differential inclusions and PDEs without uniqueness by noise
Author/s | Caraballo Garrido, Tomás
Langa Rosado, José Antonio Valero Cuadra, José |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2008 |
Deposit Date | 2015-04-08 |
Published in |
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Abstract | We prove that the asymptotic behaviour of partial differential inclusions and partial differential equations without uniqueness of solutions can be stabilised by adding some suitable Itˆo noise as an external perturbation. ... We prove that the asymptotic behaviour of partial differential inclusions and partial differential equations without uniqueness of solutions can be stabilised by adding some suitable Itˆo noise as an external perturbation. We show how the theory previously developed for the single-valued cases can be successfully applied to handle these set-valued cases. The theory of random dynamical systems is used as an appropriate tool to solve the problem. |
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