Localization of Solutions of Exterior Domain Problems for the Porous Media211 Equation with Radial Symmetry

摘要

The paper concerns the radially-symmetric Cauchy-Dirichlet and Cauchy-Neumann211u001eproblems for the porous media equation in the domain comprising the spatial 211u001evariable and the temporal variable t in the exterior of the unit ball in R(sup n) 211u001eand the bounded interval (0, T) respectively. The subject of study is the 211u001ebehavior of solutions when the initial data are compactly supported and the 211u001eboundary data become unbounded as t(up arrow)T. Necessary and sufficient 211u001econditions for localization, estimates of the size of the blow-up set, and a 211u001enumber of related results are obtained.