Analysis and Probability Seminar Sep. 16, 2014

Tuesday, September 16, 2014 (2:45-3:45 p.m. in Yost 306)

Title: Nonlinear and nonlocal evolution equations driven by Levy diffusions: an introduction

Speaker: Wojbor Woyczynski (Case Western Reserve University)

Abstract: The classical nonlinear evolution equations, such as Navier-Stokes equation , Burgers equations, and Hamilton-Jacobi-KPZ equations involve nonlinear terms and the linear part dominated by the Laplacian, the infinitesimal generator of the Brownian motion. The seminar will be a {gentle} introduction to the field of nonlinear nonlocal evolution equations when the Laplacian is replaced by the infinitesimal generator of a general Levy process which in certain situations can be  represented by a singular integral of the Riesz potential type.  The competition between the nonlinear and diffusive part will be discussed and probabilistic interpretations given.

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