11 citations · 11 across the 7 of their papers we have counts for
7 papers
Self-similar solutions to the time-fractional Porous-Medium Equation
David Gómez-Castro, Łukasz Płociniczak, Juan Luis Vázquez
We show the existence of self-similar solutions with constant finite mass to the time-fractional Porous-Medium Equation for all spatial dimensions and all exponents $m>m_…
The Fractional Stefan Problem: Global Regularity of the Bounded Selfsimilar Solution"
Marcos Llorca, Juan Luis Vázquez
We study the regularity of the bounded self-similar solution to the one-phase Stefan problem with fractional diffusion posed on the whole line. In terms of the enthalpy , t…
Asymptotic behaviour of solutions and free boundaries of the anisotropic slow diffusion equation
Filomena Feo, Juan Luis Vázquez, Bruno Volzone
In this paper we explore the theory of the anisotropic porous medium equation in the slow diffusion range. After revising the basic theory, we prove the existence of self-similar f…
A survey on mass conservation, self-similarity and related topics in nonlinear diffusion
Juan Luis Vázquez
We examine the validity of the principle of mass conservation for solutions of some typical equations in the theory of nonlinear diffusion, including equations in standard differen…
The very singular solution for the Anisotropic Fast Diffusion Equation and its consequences
Juan Luis Vázquez
We construct the Very Singular Solution (VSS) for the Anisotropic Fast Diffusion Equation (AFDE) in the suitable good exponent range of fast diffusion. VSS is a solution that, star…
Vortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility
Jose A. Carrillo, David Gómez-Castro, Juan Luis Vázquez
We consider density solutions for gradient flow equations of the form , where is the Newtonian repulsive potential in th…
Finite and infinite speed of propagation for porous medium equations with nonlocal pressure
Diana Stan, Félix del Teso, Juan Luis Vázquez
We study a porous medium equation with fractional potential pressure: for , and .…