Imperial College London
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Professor Grigorios A. Pavliotis

Faculty of Natural Sciences, Department of Mathematics

Professor of Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8564g.pavliotis Website

 
 
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Location

 

736aHuxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Pavliotis:2006,
author = {Pavliotis, G and Blomker, D and Hairer, M},
journal = {NONLINEARITY},
pages = {1721--1744},
title = {Multiscale analysis for SPDEs with quadratic nonlinearities},
url = {https://arxiv.org/abs/math/0611537v1},
year = {2006}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - In this article we derive rigorously amplitude equations for stochastic PDEs with quadratic nonlinearities, under the assumption that the noise acts only on the stable modes and for an appropriate scaling between the distance from bifurcation and the strength of the noise. We show that, due to the presence of two distinct timescales in our system, the noise (which acts only on the fast modes) gets transmitted to the slow modes and, as a result, the amplitude equation contains both additive and multiplicative noise.As an application we study the case of the one dimensional Burgers equation forced by additive noise in the orthogonal subspace to its dominant modes. The theory developed in the present article thus allows to explain theoretically some recent numerical observations from [Rob03].
AU  - Pavliotis,G
AU  - Blomker,D
AU  - Hairer,M
EP  - 1744
PY  - 2006///
SP  - 1721
TI  - Multiscale analysis for SPDEs with quadratic nonlinearities
T2  - NONLINEARITY
UR  - https://arxiv.org/abs/math/0611537v1
UR  - http://hdl.handle.net/10044/1/66626
ER  -
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