A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains

We investigate quantitative properties of the nonnegative solutions u ( t , x ) ≥ 0 to the nonlinear fractional diffusion equation, ∂ t u + L ( u m ) = 0 , posed in a bounded domain, x ∈ Ω ⊂ R N , with m  > 1 for t  > 0. As L we use one of the most common definitions of the fractional Laplacia...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2015-10, Vol.218 (1), p.317-362
Main Authors: Bonforte, Matteo, Vázquez, Juan Luis
Format: Article
Language:English
Subjects:
Classical Mechanics
Complex Systems
Fluid- and Aerodynamics
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary:We investigate quantitative properties of the nonnegative solutions u ( t , x ) ≥ 0 to the nonlinear fractional diffusion equation, ∂ t u + L ( u m ) = 0 , posed in a bounded domain, x ∈ Ω ⊂ R N , with m  > 1 for t  > 0. As L we use one of the most common definitions of the fractional Laplacian ( - Δ ) s , 0 
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-015-0861-2