From large deviations around porous media, to PDEs with irregular coefficients, to gradient flow structures
数学专题报告
报告题目(Title)：From large deviations around porous media, to PDEs with irregular coefficients, to gradient flow structures
报告人(Speaker)：Benjamin Gess (Technische Universität Berlin & Max Planck Institute)
地点(Place)：ZOOM ID: 995 8284 2944 PWD: 046828
时间(Time)：2025年11月13日（周四）16:00-17:00
邀请人(Inviter)：熊金钢
报告摘要
We consider the large deviations of the rescaled zero-range process about its hydrodynamic limit, the porous medium equation. This leads to the analysis of the skeleton equation, an energy-critical, degenerate parabolic-hyperbolic PDE with irregular drift. In this talk, we present a robust well-posedness theory for such PDEs based on concepts of renormalized solutions, the equation's kinetic form, and commutator estimates. The relationship of these large deviations principles to a formal gradient flow interpretation of the porous medium equation will be demonstrated by deducing an entropy dissipation equality from the large deviations and reversibility.
* This PDE seminar is co-organized with Tianling Jin at HKUST and Juncheng Wei at CUHK. See the seminar webpage: https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
