187 citations · 856 across the 36 of their papers we have counts for
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Behaviour near extinction for the Fast Diffusion Equation on bounded domains
Matteo Bonforte, Gabriele Grillo, Juan Luis Vazquez
We consider the Fast Diffusion Equation posed in a bounded smooth domain $Ω\subset \RR^d$ with homogeneous Dirichlet conditions; the exponent range is $m_s=(d-2)_+/(d+2)…
Degenerate homogeneous parabolic equations associated with the infinity-Laplacian
Manuel Portilheiro, Juan Luis Vázquez
We prove existence and uniqueness of viscosity solutions to the degenerate parabolic problem where is the -homogeneous operator associated with…
A porous medium equation involving the infinity-Laplacian. Viscosity solutions and asymptotic behaviour
Manuel Portilheiro, Juan Luis Vazquez
We study a nonlinear porous medium type equation involving the infinity Laplacian operator. We first consider the problem posed on a bounded domain and prove existence of maximal n…
Asymptotic behaviour of a porous medium equation with fractional diffusion
Luis Caffarelli, Juan Luis Vazquez
We consider a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. In a previous paper we have found mass-preserving, nonnegati…
A Continuum of Extinction Rates for the Fast Diffusion Equation
Marek Fila, Juan Luis Vazquez, Michael Winkler
We find a continuum of extinction rates for solutions of the fast diffusion equation in a subrange of exponents . The equation is posed in $\re…
Nonlinear porous medium flow with fractional potential pressure
Luis A. Caffarelli, Juan L. Vazquez
We study a porous medium equation, with nonlocal diffusion effects given by an inverse fractional Laplacian operator. We pose the problem in n-dimensional space for all t>0 with bo…