Mathematics – Probability
Scientific paper
2010-05-20
Stoch. Dyn. 4 (2004), no. 2, 223--244
Mathematics
Probability
18 pages, 8/9 papers from my 2000-2006 collection (preprint version)
Scientific paper
10.1142/S0219493704001024
We delve deeper into the study of semimartingale attractors that we recently introduced in Allouba and Langa \cite{AL0}. 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.
Allouba Hassan
Langa José A.
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