Existence, Uniqueness and Asymptotic behaviour for fractional porous medium equations on bounded domains
By Matteo Bonforte, Yannick Sire, Juan Luis V'azquez. 2014
196 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/267c94d85c94b81230585597a39d2f599b43e971
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In Applied Mathematics
- Juan Luis V'azquez
- Xavier Ros-Oton
- Matteo Bonforte
- Alessio Figalli
- Gerd Grubb
- G. Grillo
- Enrico Valdinoci
- A. Audrito
In Computational Theory and Mathematics
- Juan Luis V'azquez
- Matteo Bonforte
- Xavier Ros-Oton
- Gerd Grubb
- Alessio Figalli
- Enrico Valdinoci
- A. Audrito
- Nicola Garofalo
Citations in the corpus
- Regularity of spectral fractional Dirichlet and Neumann problems (2014, background): “[J02], Silvestre [S07], Caffarelli and Silvestre [CS09], Frank and Geisinger [FG14], Ros-Oton and Serra [RS14,RS15], Felsinger, Kassmann and Voigt [FKV14], Grubb [G14,G15], Bonforte, Sire and Vazquez [BSV14], Servadei and Valdinoci [SV14], and many more papers referred to in these works (see in part”
- Infinite Speed of Propagation and Regularity of Solutions to the Fractional Porous Medium Equation in General Domains (2015, background): “Let us state an existence result that follows by the results of [10] applied to the present case.”
- The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, methodology): “kernel. In the RFL we have = s. References. There is an extensive literature on the RFL operator and the corresponding -stable process in the probability literature. The interested reader is referred [46]where we have commented on relevant works in that direction. The Spectral Fractional Laplacian o”
- The Dirichlet Problem for the fractional p-Laplacian evolution equation (2015, methodology): “The Dirichlet Problem for a version of the fractional Porous Medium in a bounded domain has been recently treated by the author in collaboration with Bonforte and Sire, [9, 11].”