Regularity theory for nonlinear, degenerate partial differential equations
- Lecturer: Benjamin Gess
- Date: Monday 16:15 - 17:45
- Room: MPI MiS, A3 01
- Language: English
- Target audience: MSc students, PhD students, Postdocs
- Prerequisites: Basic PDE courses, functional analysis
In this lecture we will focus on the porous medium equation. The porous medium equation arises, for example, as a model for the flow of an ideal gas in a porous medium. The degenerate nature of the diffusivity of this PDE leads to interesting effects such as limited regularity of solutions, finite speed of propagation, open interfaces, waiting times etc. We will first recall several applications of the porous medium equation, consider special (self-similar) solutions and highlight particular properties of solutions to degenerate PDE. Then, we will focus on the question of (optimal) regularity of solutions to porous media equations, which relies on methods from harmonic analysis (Fourier multipliers, interpolation theory, Besov spaces) which will be recalled in the course of the lecture.