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Anomalous self-similar solutions of exponential type for the subcritical fast diffusion equation with weighted reaction
Razvan Gabriel Iagar, Ariel Sánchez
We prove existence and uniqueness of the branch of the so-called \emph{anomalous eternal solutions} in exponential self-similar form for the subcritical fast-diffusion equation wit…
Separate variable blow-up patterns for a reaction-diffusion equation with critical weighted reaction
Razvan Gabriel Iagar, Ariel Sánchez
We study the separate variable blow-up patterns associated to the following second order reaction-diffusion equation: posed for $x\in\mathbb{R}^N…
Eternal solutions for a reaction-diffusion equation with weighted reaction
Razvan Gabriel Iagar, Ariel Sánchez
We prove existence and uniqueness of \emph{eternal solutions} in self-similar form growing up in time with exponential rate for the weighted reaction-diffusion equation $$ \partial…
Equivalence and finite time blow-up of solutions and interfaces for two nonlinear diffusion equations
Benito Hernández-Bermejo, Razvan Gabriel Iagar, Pilar R. Gordoa +2
In this work, we construct a transformation between the solutions to the following reaction-convection-diffusion equation posed f…
Blow up profiles for a reaction-diffusion equation with critical weighted reaction
Razvan Gabriel Iagar, Ariel Sánchez
We classify the blow up self-similar profiles for the following reaction-diffusion equation with weighted reaction posed for $(x,t)\in\real\times(0…
Asymptotic behavior for the critical nonhomogeneous porous medium equation in low dimensions
Razvan Gabriel Iagar, Ariel Sánchez
We deal with the large time behavior for a porous medium equation posed in nonhomogeneous media with singular critical density $$ |x|^{-2}\partial_tu(x,t)=Δu^m(x,t), \quad (x,t)\in…
Asymptotic behavior for the heat equation in nonhomogeneous media with critical density
Razvan Iagar, Ariel Sánchez
We study the asymptotic behavior of solutions to the heat equation in nonhomogeneous media with critical singular density $$ |x|^{-2}\partial_{t}u=Δu, \quad \hbox{in} \ \real^N\tim…