Fractional nonlinear degenerate diffusion equations on bounded domains part I. Existence, uniqueness and upper bounds

We investigate quantitative properties of nonnegative solutions u(t,x)≥0 to the nonlinear fractional diffusion equation, ∂tu+LF(u)=0 posed in a bounded domain, x∈Ω⊂RN, with appropriate homogeneous Dirichlet boundary conditions. As L we can use a quite general class of linear operators that includes...

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Bibliographic Details
Published in:Nonlinear analysis 2016-01, Vol.131, p.363-398
Main Authors: Bonforte, Matteo, Vázquez, Juan Luis
Format: Article
Language:English
Subjects:
A priori estimates
Boundaries
Diffusion
Estimates
Fractional Laplacian on a bounded domain
Inequalities
Mathematical analysis
Nonlinear and nonlocal diffusion
Nonlinearity
Uniqueness
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Summary:We investigate quantitative properties of nonnegative solutions u(t,x)≥0 to the nonlinear fractional diffusion equation, ∂tu+LF(u)=0 posed in a bounded domain, x∈Ω⊂RN, with appropriate homogeneous Dirichlet boundary conditions. As L we can use a quite general class of linear operators that includes the two most common versions of the fractional Laplacian (−Δ)s, 0
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2015.10.005