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 …

We construct the fundamental solution of the Porous Medium Equation posed in the
hyperbolic space H n and describe its asymptotic behavior as t→∞. We also show that it …

We study weighted porous media equations on domains $\Omega\subseteq {\mathbb R}^ N
$, either with Dirichlet or with Neumann homogeneous boundary conditions when …

We consider nonnegative solutions of the porous medium equation (PME) on Cartan–
Hadamard manifolds whose negative curvature can be unbounded. We take compactly …

We study a priori estimates for a class of non-negative local weak solution to the weighted
fast diffusion equation ut=| x| γ∇⋅(| x|− β∇ um), with 0< m< 1 posed on cylinders of (0, T)× R …

We prove existence and uniqueness of solutions to a class of porous media equations
driven by the fractional Laplacian when the initial data are positive finite Radon measures …

We investigate fine global properties of nonnegative, integrable solutions to the Cauchy
problem for the fast diffusion equation with weights (WFDE) ut D jxj div. jxj ˇ rum/posed on. 0; …

We are concerned with the long time behaviour of solutions to the fractional porous medium
equation with a variable spatial density. We prove that if the density decays slowly at infinity …

We study existence of global solutions and finite time blow-up of solutions to the Cauchy
problem for the porous medium equation with a variable density ρ (x) and a power-like …

This paper is the second part of the study. In Part~ I, self-similar solutions of a weighted fast
diffusion equation (WFD) were related to optimal functions in a family of subcritical Caffarelli …