Asymptotic Dynamics of Stochastic p-Laplace Equations on Unbounded Domains

2014/08/03 by Krause, Andrew
#35B40 (Primary) 35B41 #37L30 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1408.0520

Abstract

This thesis is concerned with the asymptotic behavior of solutions of stochastic p-Laplace equations driven by non-autonomous forcing on ℝⁿ. Two cases are studied, with additive and multiplicative noise respectively. Estimates on the tails of solutions are used to overcome the non-compactness of Sobolev embeddings on unbounded domains, and prove asymptotic compactness of solution operators in L²(ℝⁿ). Using this result we prove the existence and uniqueness of random attractors in each case. Additionally, we show the upper semicontinuity of the attractor for the multiplicative noise case as the intensity of the noise approaches zero.

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