Diffusion approximation for self-similarity of stochastic advection in Burgers’ equation
Date
2015
Authors
Wang, W.
Roberts, A.
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Journal article
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Communications in Mathematical Physics, 2015; 333(3):1287-1316
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Wei Wang, A.J. Roberts
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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.
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© Springer-Verlag Berlin Heidelberg 2014