187 citations · 856 across the 36 of their papers we have counts for
4 papers · 2 filters
Regularity of solutions of the fractional porous medium flow with exponent 1/2
Luis Caffarelli, Juan Luis Vázquez
We study the regularity of a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. The precise model is $u_t=\nabla\cdot(u\nabla…
Fundamental solution and long time behaviour of the Porous Medium Equation in Hyperbolic Space
Juan Luis Vazquez
We construct the fundamental solution of the Porous Medium Equation posed in the hyperbolic space and describe its asymptotic behaviour as . We also show that it…
Existence, Uniqueness and Asymptotic behaviour for fractional porous medium equations on bounded domains
Matteo Bonforte, Yannick Sire, Juan Luis Vazquez
We consider nonlinear diffusive evolution equations posed on bounded space domains, governed by fractional Laplace-type operators, and involving porous medium type nonlinearities.…
The Mesa Problem for the Fractional Porous Medium Equation
Juan Luis Vázquez
We investigate the behaviour of the solutions of the fractional porous medium equation with initial data $u(x…