2014/04/24 by Matteo Bonforte, Yannick Sire, Bonforte, Matteo +2 · 3 citations
Computer Science · Mathematics · #35A01 #35A02 #35B40 #35K55 #35K61 #35K65 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1404.6195
openalex publication_date 2014/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider nonlinear diffusive evolution equations posed on bounded space\ndomains, governed by fractional Laplace-type operators, and involving porous\nmedium type nonlinearities. We establish existence and uniqueness results in a\nsuitable class of solutions using the theory of maximal monotone operators on\ndual spaces. Then we describe the long-time asymptotics in terms of\nseparate-variables solutions of the friendly giant type. As a by-product, we\nobtain an existence and uniqueness result for semilinear elliptic non local\nequations with sub-linear nonlinearities. The Appendix contains a review of the\ntheory of fractional Sobolev spaces and of the interpolation theory that are\nused in the rest of the paper.\n