Attractors for stochastic reaction-diffusion equation with additive homogeneous noise

0536375 - ÚTIA 2022 RIV CZ eng J - Journal Article
Slavík, Jakub
Attractors for stochastic reaction-diffusion equation with additive homogeneous noise.
Czechoslovak Mathematical Journal. Roč. 71, č. 1 (2021), s. 21-43. ISSN 0011-4642. E-ISSN 1572-9141
Institutional support: RVO:67985556
Keywords : reaction-diffusion equation * random attractor * spatially homogeneous noise
OECD category: Statistics and probability
Impact factor: 0.328, year: 2021
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2020/SI/slavik-0536375.pdf https://link.springer.com/article/10.21136/CMJ.2020.0144-19

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.
Permanent Link: http://hdl.handle.net/11104/0314165