4 papers
Self-similar solutions to the time-fractional Porous-Medium Equation
David Gómez-Castro, Åukasz PÅociniczak, 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_…
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 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…