Séminaire d'AnalyseOn nonlocal (and local) equations of porous medium type
jeudi 19 septembre 2019 10:30 - Tours - Salle 1180 (Bât E2)
We study uniqueness, existence, and properties of bounded distributional (very weak) solutions of generalized porous medium type equations. Here the diffusion operator can be any symmetric (possibly $x$-dependent) degenerate elliptic operator including the Laplacian, the fractional Laplacian, and numerical discretizations of either. The nonlinearity is only assumed to be continuous and nondecreasing. This class of Cauchy problems include porous medium equations, fast diffusion equations, and (one-phase) Stefan problems. We will also consider numerical schemes (and simulations) of these equations.