scholarly journals Deterministic particle approximation of aggregation-diffusion equations on unbounded domains

2022 ◽  
Vol 312 ◽  
pp. 474-517
Author(s):  
Sara Daneri ◽  
Emanuela Radici ◽  
Eris Runa
Keyword(s):  
Unbounded Domains ◽  
Diffusion Equations ◽  
Particle Approximation

Limit measures and ergodicity of fractional stochastic reaction–diffusion equations on unbounded domains

2021 ◽  
pp. 2140012
Author(s):  
Zhang Chen ◽  
Bixiang Wang
Keyword(s):  
Invariant Measures ◽  
Unbounded Domains ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Lipschitz Continuous ◽  
Bounded Interval ◽  
Locally Lipschitz ◽  
Stochastic Reaction ◽  
And Diffusion

This paper deals with invariant measures of fractional stochastic reaction–diffusion equations on unbounded domains with locally Lipschitz continuous drift and diffusion terms. We first prove the existence and regularity of invariant measures, and then show the tightness of the set of all invariant measures of the equation when the noise intensity varies in a bounded interval. We also prove that every limit of invariant measures of the perturbed systems is an invariant measure of the corresponding limiting system. Under further conditions, we establish the ergodicity and the exponentially mixing property of invariant measures.

Comparison principles for strongly coupled reaction diffusion equations in unbounded domains

1988 ◽  
Vol 110 (3-4) ◽  
pp. 311-319 ◽  
Author(s):  
E. Tuma
Keyword(s):  
Unbounded Domains ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Nerve Fibres ◽  
Strongly Coupled ◽  
Comparison Principles ◽  
Nagumo Equations ◽  
And Diffusion ◽  
Coupled Reaction

SynopsisComparison principles for systems of reaction–diffusion equations in unbounded domains and coupledvia both reaction and diffusion terms are considered. Applications are made to the FitzHugh–Nagumo equations and models of coupled nerve fibres.

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