The porous medium equation: Large deviations and gradient flow with degenerate and unbounded diffusion

• Published in: Communications on pure and applied mathematics Vol. 78; no. 9; pp. 1609 - 1655
• Main Authors: Gess, Benjamin, Heydecker, Daniel
• Format: Journal Article
• Language: English
• Published: New York John Wiley and Sons, Limited 01.09.2025
• Subjects: Deviation; Gradient flow; Porous media; Thermodynamics
• ISSN: 0010-3640; 1097-0312
• DOI: 10.1002/cpa.22251

The problem of deriving a gradient flow structure for the porous medium equation which is thermodynamic, in that it arises from the large deviations of some microscopic particle system is studied. To this end, a rescaled zero‐range process with jump rate g(k)=kα,α>1$g(k)=k^\alpha, \alpha >1$ i...