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CCF Seminar
Jin Feng University of Kansas Title: A class of Hamilton-Jacobi PDE in space of measures and its associated compressible Euler equations Abstract: We introduce a class of action integrals defined over probability measure-valued path space. We show that minimal action exists and satisfies a compressible Euler equation in weak sense. Moreover, we prove that both Cauchy and resolvent formulations of the associated Hamilton-Jacobi equation, in the space of probability measures, are well posed. In addition to technical issues in optimal control and modern mass transport theories, there are two key arguments which involves relaxation and regularization in formulation of the problem. They are both rooted in questions from probability. In particular, from a large deviation theory point of view,the regularization we introduced is a natural way to define entropic solution in path space. This is a joint work with Truyen Nguyen. |