Czechoslovak Mathematical Journal, Vol. 71, No. 1, pp. 21-43, 2021


Attractors for stochastic reaction-diffusion equation with additive homogeneous noise

Jakub Slavík

Received March 28, 2019.   Published online August 18, 2020.

Abstract:  We study the asymptotic behaviour of solutions of a reaction-diffusion equation in the whole space $\Rd$ driven by a spatially homogeneous Wiener process with finite spectral measure. The existence of a random attractor is established for initial data in suitable weighted $L^2$-space in any dimension, which complements the result from P. W. Bates, K. Lu, and B. Wang (2013). Asymptotic compactness is obtained using elements of the method of short trajectories.
Keywords:  reaction-diffusion equation; random attractor; spatially homogeneous noise
Classification MSC:  35B41, 60H15, 37L55, 35K57


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Affiliations:   Jakub Slavík, Institute of Information Theory and Automation, Czech Academy of Sciences, Pod Vodárenskou věží 4, 182 00 Praha 8, Czech Republic, e-mail: slavik@utia.cas.cz


 
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