Open AccessPeriodic measures of reaction-diffusion lattice systems driven by superlinear noise
Author(s) -
Yusen Lin,
AUTHOR_ID
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022002
Subject(s) - lattice (music) , reaction–diffusion system , mathematics , statistical physics , crystal system , diffusion , pure mathematics , physics , mathematical analysis , chemistry , quantum mechanics , crystallography , crystal structure , acoustics
The periodic measures are investigated for a class of reaction-diffusion lattice systems driven by superlinear noise defined on $ \mathbb Z^k $. The existence of periodic measures for the lattice systems is established in $ l^2 $ by Krylov-Bogolyubov's method. The idea of uniform estimates on the tails of solutions is employed to establish the tightness of a family of distribution laws of the solutions.