R. Iagar

Peaking self-similar solutions and continuation after blow-up for a quasilinear Hardy-Hénon equation

Razvan Gabriel Iagar, Ariel Sánchez, Erik Sarrión-Pedralva

We consider the quasilinear Hardy-Hénon equation $u_{t} = Δ u^{m} + ∣ x ∣^{σ} u^{p}, (x, t) \in R^{N} \times (0, T),$ in the range of exponents and dimension $$ N\geq3, \quad σ\in(-2,\i…

A porous medium equation with dominating weighted absorption: three types of self-similar solutions

Razvan Gabriel Iagar, Diana-Rodica Munteanu

Self-similar solutions to the porous medium equation with dominating spatially inhomogeneous absorption $$ \partial_tu=Δu^m-|x|^σu^p, \quad (x,t)\in\real^N\times(0,\infty), \quad N…

Convergence to self-similarity for a degenerate parabolic equation with fast-growing spatially-dependent absorption

Razvan Gabriel Iagar, Philippe Laurençot

The large time behavior of non-negative solutions to the absorption-diffusion equation $\partial$ \textsubscr{t} u = $Δ$ u\textsuperscript{m} - |x|\textsuperscript{ $σ$ }u\textsupers…

Boundedness and evolution rates for a quasilinear reaction-diffusion equation

Razvan Gabriel Iagar, Marta Latorre, Ariel Sánchez

We consider the following quasilinear reaction-diffusion equation $\partial_{t} u = Δ u^{m} + (1 + ∣ x ∣)^{σ} u^{p}, (x, t) \in R^{N} \times (0, \infty),$ in dimension $N \geq 3$ and in the…

Large time behavior and transition from vanishing to spreading regimes for the generalized Burgers-Fisher-KPP equation

Razvan Gabriel Iagar, Ariel Sánchez

The large time behavior of solutions to the following generalized Burgers-Fisher-KPP equation $\partial_{t} u = u_{xx} + k (u^{n})_{x} + u^{p} - u^{q}, (x, t) \in R \times (0, \infty),$ w…

Blow-up rates and sets for a quasilinear diffusion equation with weighted source

Raúl Ferreira, Razvan Gabriel Iagar, Ariel Sánchez

Blow-up rates are established for general solutions to the quasilinear diffusion equation $\partial_{t} u = Δ u^{m} + ∣ x ∣^{σ} u^{p}, (x, t) \in R^{N} \times (0, T),$ in the range of ex…

Global self-similar solutions for Hardy-Hénon equations with linear and quasilinear diffusion

Razvan Gabriel Iagar, Ariel Sánchez, Erik Sarrion-Pedralva

Global self-similar solutions to the parabolic Hardy-Hénon equation $u_{t} = Δ u^{m} + ∣ x ∣^{σ} u^{p}, (x, t) \in R^{N} \times (0, \infty),$ are classified in the range of exponents $m…

Self-similar extinction for a fast diffusion equation with weighted absorption

Razvan Gabriel Iagar, Diana-Rodica Munteanu

Finite time extinction of any bounded solution to the fast diffusion equation with spatially inhomogeneous absorption $$ \partial_tu=Δu^m-|x|^σu^p, \quad (x,t)\in\mathbb{R}^N\times…

Self-similar blow-up solutions for the supercritical parabolic Hardy-Hénon equation

Razvan Gabriel Iagar, Ana I. Muñoz, Ariel Sánchez

We classify the self-similar solutions presenting finite time blow-up to the parabolic Hardy-Hénon equation $$ \partial_tu=Δu+|x|^σu^p, \quad (x,t)\in\mathbb{R}^N\times(0,\infty),…

Traveling wave solutions for the generalized Burgers-Fisher equation

Razvan Gabriel Iagar, Ariel Sánchez

Traveling wave solutions, in the form $u (x, t) = f (x + c t)$ , to the generalized Burgers-Fisher equation $$ \partial_tu=u_{xx}+k(u^n)_x+u^p-u^q, \quad (x,t)\in\mathbb{R}\times(0,\infty),…

A porous medium equation with spatially inhomogeneous absorption. Part II: Large time behavior

Razvan Gabriel Iagar, Diana-Rodica Munteanu

We study the large time behavior of solutions to the Cauchy problem for the quasilinear absorption-diffusion equation $$ \partial_tu=Δu^m-|x|^σu^p, \quad (x,t)\in\real^N\times(0,\i…

Sharp non-existence threshold for a parabolic Hardy-H{é}non equation with quasilinear diffusion

Razvan Gabriel Iagar, Philippe Laurençot

Optimal conditions for initial data leading to non-existence of non-negative solutions to the Cauchy problem for the parabolic Hardy-H{é}non equation $$ \partial\_tu=Δu^m+|x|^σu^p,…

Large time behavior for a quasilinear diffusion equation with weighted source

Razvan Gabriel Iagar, Marta Latorre, Ariel Sánchez

The large time behavior of general solutions to a class of quasilinear diffusion equations with a weighted source term $$ \partial_tu=Δu^m+\varrho(x)u^p, \quad (x,t)\in\mathbb{R}^N…

A parabolic Hardy-Hénon equation with quasilinear degenerate diffusion

Razvan Gabriel Iagar, Philippe Laurençot

Local and global well-posedness, along with finite time blow-up, are investigated for the following Hardy-Hénon equation involving a quasilinear degenerate diffusion and a space-de…

A new transformation for the subcritical fast diffusion equation with source and applications

Razvan Gabriel Iagar, Ariel Sánchez

A new transformation for radially symmetric solutions to the subcritical fast diffusion equation with spatially inhomogeneous source $\partial_{t} u = Δ u^{m} + ∣ x ∣^{σ} u^{p},$ posed for $(x,…

math.AP2024★ 2 cited

A critical non-homogeneous heat equation with weighted source

Razvan Gabriel Iagar, Ariel Sánchez

Some qualitative properties of radially symmetric solutions to the non-homogeneous heat equation with critical density and weighted source $$ |x|^{-2}\partial_tu=Δu+|x|^σu^p, \quad…

Qualitative properties of solutions to a generalized Fisher-KPP equation

Razvan Gabriel Iagar, Ariel Sánchez

The following Fisher-KPP type equation $u_{t} = K u_{xx} - B u^{q} + A u^{p}, (x, t) \in ℜ \times (0, \infty),$ with $p > q > 0$ and $A$ , $B$ , $K$ positive coefficients, is considered. For bo…

A Hardy-H{é}non equation in $R^{N}$ with sublinear absorption

Razvan Gabriel Iagar, Philippe Laurençot

Consider $m & g t; 1$ , $N \geq 1$ and $\max\{-2,-N\}\<σ\<0$. The Hardy-Hénon equation with sublinear absorption\begin(equation*}- Δv(x) - |x|^σv(x) + \frac{1}{m-1} v^{1/m}(x)= 0, \qquad…

Eternal solutions to a porous medium equation with strong nonhomogeneous absorption. Part II: Dead-core profiles

Razvan Gabriel Iagar, Philippe Laurençot, Ariel Sánchez

Existence of a specific family of \emph{eternal solutions} in exponential self-similar form is proved for the following porous medium equation with strong absorption $$\partial_t u…

Second order asymptotics and uniqueness for self-similar profiles to a singular diffusion equation with gradient absorption

Razvan Gabriel Iagar, Philippe Laurençot

Solutions in self-similar form presenting finite time extinction to the singular diffusion equation with gradient absorption $$\partial_t u - \mathrm{div}(|\nabla u|^{p-2}\nabla u)…

A porous medium equation with spatially inhomogeneous absorption. Part I: Self-similar solutions

Razvan Gabriel Iagar, Diana Rodica Munteanu

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 $$…