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

2015
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Archive for Rational Mechanics and Analysis
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We investigate quantitative properties of 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 for t > 0 and m > 1. As L we can take the most common definitions of the fractional Laplacian (−∆) s , 0 < s < 1, in a bounded domain with zero Dirichlet boundary conditions, as well as more general classes of operators. We consider a class of very weak solutions for the equation at hand, that we call weak dual

doi:10.1007/s00205-015-0861-2
fatcat:cfwell5n7bbaheb5ftt2cg5xyu