Localization of solutions of exterior domain problems for the porous media equation with radial symmetry

摘要

The paper concerns the radially symmetric Cauchy-Dirichlet and Cauchy-Neumann problems for the porous media equation in the domain comprising the spatial variable and the temporal variable t in the exterior of the unit ball in R-n and the bounded interval (0, T), respectively. The subject of study is the behavior of solutions when the initial data are compactly supported and the boundary data become unbounded as t up arrow T. Necessary and sufficient conditions for localization, estimates of the size of the blow-up set, and a number of allied results are obtained. [References: 40]