Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 35, Issue 12, Pages 5725-5767Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2015.35.5725
Keywords
Fractional Laplace operators; porous medium diffusion; existence and uniqueness theory; asymptotic behaviour; fractional Sobolev spaces
Categories
Funding
- ANR
- [MTM2011-24696]
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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.
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