# American Institute of Mathematical Sciences

December  2015, 35(12): 5725-5767. doi: 10.3934/dcds.2015.35.5725

## Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains

 1 Departamento de Matemáticas, Universidad Autónoma de Madrid, Campus de Cantoblanco, 28049 Madrid, Spain, Spain 2 Université Aix-Marseille, I2M, Centre de Mathématique et Informatique, Technopôle de Chateau-Giombert, Marseille, France

Received  April 2014 Published  May 2015

We consider nonlinear diffusive evolution equations posed on bounded space domains, governed by fractional Laplace-type operators, and involving porous medium type nonlinearities. We establish existence and uniqueness results in a suitable class of solutions using the theory of maximal monotone operators on dual spaces. Then we describe the long-time asymptotics in terms of separate-variables solutions of the friendly giant type. As a by-product, we obtain an existence and uniqueness result for semilinear elliptic non local equations with sub-linear nonlinearities. The Appendix contains a review of the theory of fractional Sobolev spaces and of the interpolation theory that are used in the rest of the paper.
Citation: Matteo Bonforte, Yannick Sire, Juan Luis Vázquez. Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains. Discrete & Continuous Dynamical Systems, 2015, 35 (12) : 5725-5767. doi: 10.3934/dcds.2015.35.5725
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