Diffusion approximation for self-similarity of stochastic advection in Burgers' equation

Details Diffusion approximation for self-similarity of stochastic advection in Burgers' equation Diffusion approximation for self-similarity of stochastic advection in Burgers' equation

2012-03-02

arxiv.org/abs/1203.0463v1

Mathematics

Analysis of PDEs

32 pages

Scientific paper

Self-similarity of Burgers' equation with some 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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