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Type: Journal article
Title: Diffusion approximation for self-similarity of stochastic advection in Burgers’ equation
Author: Wang, W.
Roberts, A.
Citation: Communications in Mathematical Physics, 2015; 333(3):1287-1316
Publisher: Springer
Issue Date: 2015
ISSN: 0010-3616
Statement of
Wei Wang, A.J. Roberts
Abstract: Self-similarity of Burgers’ equation with stochastic advection is studied. In self-similar variables a stationary solution is constructed which establishes the existence of a stochastically self-similar solution for the stochastic Burgers’ equation. The analysis assumes that the stochastic coefficient of advection is transformed to a white noise in the self-similar variables. Furthermore, by a diffusion approximation, the long time convergence to the self-similar solution is proved in the sense of distribution.
Rights: © Springer-Verlag Berlin Heidelberg 2014
DOI: 10.1007/s00220-014-2117-7
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Mathematical Sciences publications

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