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Semimartingale attractors for Allen-Cahn SPDEs driven by space-time white noise I: existence and finite dimensional asymptotic behavior

Opened Access Semimartingale attractors for Allen-Cahn SPDEs driven by space-time white noise I: existence and finite dimensional asymptotic behavior

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Autor: Allouba, Hassan
Langa Rosado, José Antonio
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2004
Publicado en: Stochastics and Dynamics, 4 (2), 223-244.
Tipo de documento: Artículo
Resumen: We delve deeper into the study of semimartingale attractors that we recently introduced in Allouba and Langa [4] H. Allouba and J.A. Langa, Semimartingale attractors for generalized Allen-Cahn SPDEs driven by space-time white noise, C. R. Acad. Sci. Paris, Ser. I 337 (2003), 201-206. In this article we focus on second order SPDEs of the Allen-Cahn type. After proving existence, uniqueness, and detailed regularity results for our SPDEs and a corresponding random PDE of Allen-Cahn type, we prove the existence of semimartingale global attractors for these equations. We also give some results on the finite dimensional asymptotic behavior of the solutions. In particular, we show the finite fractal dimension of this random attractor and give a result on determining modes, both in the forward and the pullback sense.
Cita: Allouba, H. y Langa Rosado, J.A. (2004). Semimartingale attractors for Allen-Cahn SPDEs driven by space-time white noise I: existence and finite dimensional asymptotic behavior. Stochastics and Dynamics, 4 (2), 223-244.
Tamaño: 261.7Kb
Formato: PDF

URI: http://hdl.handle.net/11441/44987

DOI: 10.1142/S0219493704001024

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