We classify all the blow-up solutions in self-similar form to the following reaction-diffusion
equation\partial_tu= Δ u^ m+| x|^ σ u^ p, posed for (x,t)∈R^N*(0,T), with m>1, 1≦p<m and …

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 classify the finite time blow-up profiles for the following reaction-diffusion equation with
unbounded weight: $$\partial_tu=\Delta u^ m+| x|^{\sigma} u^ p, $$ posed in any space …

Existence and uniqueness of a specific self-similar solution is established for the following
reaction-diffusion equation with Hardy singular potential∂ tu= Δ u m+| x|− 2 up,(x, t)∈ …

We prove existence and uniqueness of the branch of the so-called anomalous eternal
solutions in exponential self-similar form for the subcritical fast-diffusion equation with a …

The non-existence of nonnegative finite energy solutions to− Δ V (x)−| x| σ V (x)+ V 1/m (x)
m− 1= 0, x∈ RN, with m> 1, σ> 0, and N≥ 1, is proven for σ sufficiently large. More …

We establish both extinction and non-extinction self-similar profiles for the following fast
diffusion equation with a weighted source term $$\partial_tu=\Delta u^ m+| x|^{\sigma} u^ p …

We classify radially symmetric self-similar profiles presenting finite time blow-up to the
quasilinear diffusion equation with weighted source $$ u_t=\Delta u^ m+| x|^{\sigma} u^ p …

This is the first of a two-parts work on the qualitative properties and large time behavior for
the following quasilinear equation involving a spatially inhomogeneous absorption …

Solutions in self-similar form, either global in time or presenting finite time blow-up, to the
fast diffusion equation with spatially inhomogeneous source $$\partial_tu=\Delta u^ m+ …