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2009 Amplitude Equation for SPDEs with Quadratic Non-Linearities
Dirk Blömker, Wael mohammed
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Electron. J. Probab. 14: 2527-2550 (2009). DOI: 10.1214/EJP.v14-716


In this paper we rigorously derive stochastic amplitude equations for a rather general class of SPDEs with quadratic nonlinearities forced by small additive noise. Near a change of stability we use the natural separation of time-scales to show that the solution of the original SPDE is approximated by the solution of an amplitude equation, which describes the evolution of dominant modes. Our results significantly improve older results. We focus on equations with quadratic nonlinearities and give applications to the one-dimensional Burgers’ equation and a model from surface growth.


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Dirk Blömker. Wael mohammed. "Amplitude Equation for SPDEs with Quadratic Non-Linearities." Electron. J. Probab. 14 2527 - 2550, 2009.


Accepted: 13 November 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1197.60061
MathSciNet: MR2563250
Digital Object Identifier: 10.1214/EJP.v14-716

Primary: 60H15
Secondary: 35K35 , 35Q99 , 35R60 , 60H10

Keywords: Amplitude equations , quadratic nonlinearities , separation of time- scales , SPDE

Vol.14 • 2009
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