Geodesic
Attractors for stochastic reaction-diffusion equation with additive homogeneous noise
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 21-43.

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We study the asymptotic behaviour of solutions of a reaction-diffusion equation in the whole space $\mathbb{R}^d$ 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.
DOI : 10.21136/CMJ.2020.0144-19
Classification : 35B41, 35K57, 37L55, 60H15
Keywords: reaction-diffusion equation; random attractor; spatially homogeneous noise 
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Slavík, Jakub. Attractors for stochastic reaction-diffusion equation with additive homogeneous noise. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 21-43. doi : 10.21136/CMJ.2020.0144-19. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0144-19/

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