Attractors for stochastic reaction-diffusion equation with additive homogeneous noise

Jakub Slavík

Czechoslovak Mathematical Journal (2021)

  • Issue: 1, page 21-43
  • ISSN: 0011-4642

Abstract

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We study the asymptotic behaviour of solutions of a reaction-diffusion equation in the whole space 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.

How to cite

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Slavík, Jakub. "Attractors for stochastic reaction-diffusion equation with additive homogeneous noise." Czechoslovak Mathematical Journal (2021): 21-43. <http://eudml.org/doc/297347>.

@article{Slavík2021,
abstract = {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.},
author = {Slavík, Jakub},
journal = {Czechoslovak Mathematical Journal},
keywords = {reaction-diffusion equation; random attractor; spatially homogeneous noise},
language = {eng},
number = {1},
pages = {21-43},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Attractors for stochastic reaction-diffusion equation with additive homogeneous noise},
url = {http://eudml.org/doc/297347},
year = {2021},
}

TY - JOUR
AU - Slavík, Jakub
TI - Attractors for stochastic reaction-diffusion equation with additive homogeneous noise
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 21
EP - 43
AB - 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.
LA - eng
KW - reaction-diffusion equation; random attractor; spatially homogeneous noise
UR - http://eudml.org/doc/297347
ER -

References

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