Fast-Diffusion Limit with Large Noise for Systems of Stochastic Reaction-Diffusion Equations

  • We consider a class of stochastic reaction-diffusion equations with additive noise. We show that in the limit of fast diffusion, one can approximate solutions of the SPDE by the solution of a suitable ordinary differential equation (ODE) only describing the reactions. Also, we show large fluctuations lead in the limit to surprising new terms in the ODE. We focus on systems with polynomials nonlinearities and give applications to the predator-prey system and a cubic auto-catalytic reaction between two chemicals.

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Author:Wael W. MohammedGND, Dirk BlömkerORCiDGND
Frontdoor URL
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2014-03)
Year of first Publication:2014
Publishing Institution:Universität Augsburg
Release Date:2014/04/07
Tag:stochastic partial differential equations; fast diffusion; averaging; large noise
GND-Keyword:Stochastische partielle Differentialgleichung; Diffusionsprozess; Reaktions-Diffusionsgleichung; Rauschen
Erschienen in Stochastic Analysis and Applications, 34, 6, S. 961-978,
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand