School Colloquium (On Friday) ——Solutions of SPDE as zeros of maps on scaled path spaces
主 题: School Colloquium (On Friday) ——Solutions of SPDE as zeros of maps on scaled path spaces
报告人: Professor Roeckner (Bielefeld University,Germany)
时 间: 2018-03-09 15:00-16:00
地 点: Room 1114, Sciences Building No. 1
Abstract: It has been recently shown that the solutions of a large class of stochastic partial differential equations (SPDE) can be obtained as zeros of a properly defined map on a path space equipped with a norm which is “scaled“ by the exponential of a function-valued Brownian motion. In the talk this result will be reviewed and connected to current developments about the case where the underlying SPDE is a gradient flow, perturbed by linear multiplicative noise. In this case it follows from the above result and by applying methods from the calculus of variations that the solution minimizes a certain explicit convex functional on the path space. Applications include stochastic porous media equations, stochastic nonlinear parabolic equations (as e.g. the stochastic Cauchy problem for the p-Laplacian) and in the non-gradient case also stochastic nonlinear transport equations.