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 |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-26762 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/2676 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2014-03) |
| Type: | Preprint |
| Language: | English |
| 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 |
| Note: | Erschienen in Stochastic Analysis and Applications, 34, 6, S. 961-978, https://doi.org/10.1080/07362994.2016.1197131 |
| 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 |
