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

B.H. Gilding, J. Goncerzewicz

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Abstract

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 ${\mathbb{R}}^n$ and the bounded interval $(0,T)$ respectively. The subject of study is the behaviour of solutions when the initial data are compactly supported and the boundary data become unbounded as $t \uparrow T$. Necessary and sufficient conditions for localization, estimates of the size of the blow-up set, and a number of related results are obtained.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Publication statusPublished - 1998

Keywords

  • MSC-35B99
  • MSC-35K55
  • EWI-3268
  • MSC-35R35
  • MSC-35K65

Cite this

Gilding, B. H., & Goncerzewicz, J. (1998). Localization of solutions of exterior domain problems for the porous media equation with radial symmetry. Enschede: University of Twente, Department of Applied Mathematics.