Special Session 123: Nonlinear phenomena in elliptic and parabolic equations

Solvability of the Cauchy problem for the porous medium equation with singular initial data
Nobuhito Miyake
Faculty of Mathematics, Kyushu University
Japan
Co-Author(s):    Kazuhiro Ishige, Ryuichi Sato
Abstract:
We consider the solvability of the Cauchy problem for the porous medium equation with a power-type nonlinearity. More precisely, we establish a sufficient condition on the initial data for the existence of solutions in terms of uniformly local Morrey-type spaces. As an application, we identify the optimal singular profile of the initial data for solvability. This talk is based on the joint work with Kazuhiro Ishige (the University of Tokyo) and Ryuichi Sato (Iwate University).