### 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 language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 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.