Infinite Speed of Propagation and Regularity of Solutions to the Fractional Porous Medium Equation in General Domains

By Matteo Bonforte, Alessio Figalli, Xavier Ros-Oton. 2015

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We study the positivity and regularity of solutions to the fractional porous medium equations ut+(−Δ)sum=0 in (0,∞)×Ω for m > 1 and s ∈ (0,1), with Dirichlet boundary data u = 0 in (0,∞)×(ℝN∖Ω) and nonnegative initial condition u(0,⋅)=u0≥0 .

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

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