70 citations · 313 across the 31 of their papers we have counts for
4 papers · 2 filters
Porous medium equation with nonlocal pressure in a bounded domain
Quoc-Hung Nguyen, Juan Luis Vázquez
We study a quite general family of nonlinear evolution equations of diffusive type with nonlocal effects. More precisely, we study porous medium equations with a fractional Laplaci…
Asymptotic behaviour for the Fractional Heat Equation in the Euclidean space
Juan Luis Vázquez
We consider weak solutions of the fractional heat equation posed in the whole -dimensional space, and establish their asymptotic convergence to the fundamental solution as $t\to…
The mathematical theories of diffusion. Nonlinear and fractional diffusion
Juan Luis Vázquez
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic m…
Asymptotic behaviour methods for the Heat Equation. Convergence to the Gaussian
Juan Luis Vázquez
In this expository work we discuss the asymptotic behaviour of the solutions of the classical heat equation posed in the whole Euclidean space. After an introductory review of the…