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Attractors for Stochastic Reaction-Diffusion Equation with Additive Homogeneous Noise

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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 L2-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.

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Acknowledgement

The author wishes to thank J. Seidler for discussions leading to the results of this paper and M. Ondreját for simplification of several important arguments.

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Authors and Affiliations

  1. Institute of Information Theory and Automation, Czech Academy of Sciences, Pod Vodárenskou vezí 4, 182 00, Praha 8, Czech Republic

    Jakub Slavík

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  1. Jakub Slavík
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Correspondence to Jakub Slavík.

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Slavík, J. Attractors for Stochastic Reaction-Diffusion Equation with Additive Homogeneous Noise. Czech Math J 71, 21–43 (2021). https://doi.org/10.21136/CMJ.2020.0144-19

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