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 prove existence and uniqueness of a global in time self-similar solution growing up as
t→∞ for the following reaction-diffusion equation with a singular potential ut= Δ u m+| x| σ …

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

On the Cauchy problem for a general fractional porous medium equation with variable density
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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 study two classes of degenerate parabolic equations of the forms where λ> 0, m+ λ− 2>
0 and a (s) and ρ (s) are positive continuous functions on (0,∞). We examine under which …

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 …