| Abstract: |
| We consider the porous medium equation in the complement of a bounded domain with zero Dirichlet data on its boundary and nonnegative compactly supported integrable initial data.
Kamin and V\`azquez, in 1991, studied the large time behavior of solutions of such problem in space dimension 1. Gilding and Goncerzewicz, in 2007, studied this same problem dimension 2. Using their results in the outer field we study the large time behavior of the solution in the near field scale, in particular in bounded sets of the domain.
This a joint work with Fernando Quir\`os ( Universidad Autonoma de Madrid, Spain) and Noem\`i Wolanski ( Universidad de Buenos Aires, Argentina). |
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