Abraham Solar

activity

20142021

most citedAsymptotic convergence to pushed wavefronts in a monostable equation with delayed reaction

12 citations · 38 across the 7 of their papers we have counts for

collaborators

8 papers

math.AP2021

Wavefront's stability with asymptotic phase in the delayed monostable equations

Abraham Solar, Sergei Trofimchuk

We extend the class of initial conditions for scalar delayed reaction-diffusion equations $u_{t} (t, x) = u_{xx} (t, x) + f (u (t, x), u (t - h, x))$ which evolve in solutions converging to mono…

math.AP2018

Stability of non-monotone and backward waves for delay non-local reaction-diffusion equations

Abraham Solar

This paper deals with the stability of semi-wavefronts to the following delay non-local monostable equation: $\dot{v}(t,x) = Δv(t,x) - v(t,x) + \int_{\R^d}K(y)g(v(t-h,x-y))dy, x \i…

math.CA2018★ 10 cited

A simple approach to the wave uniqueness problem

Abraham Solar, Sergei Trofimchuk

We propose a new approach for proving uniqueness of semi-wavefronts in generally non-monotone monostable reaction-diffusion equations with distributed delay. This allows to solve a…

math.AP2018

An iterative estimation for disturbances of semi-wavefronts to the delayed Fisher-KPP equation

Rafael Benguria D., Abraham Solar

We give an iterative method to estimate the disturbance of semi-wavefronts of the equation: $u ˙ (t, x) = u^{''} (t, x) + u (t, x) (1 - u (t - h, x)),$ $x \in R, t > 0;$ where $h > 0.$ A…

math.AP2018★ 5 cited

An estimation of level sets for non local KPP equations with delay

Rafael Benguria, Abraham Solar

We study the large time asymptotic behavior of the solutions of the linear parabolic equation with delay $(*)$ : $u_{t}(t,x) = u_{xx}(t,x) - u(t,x) + \int_{\mathbb{R}} k(x-y) \, u (…

math.AP2017

Stability of semi-wavefronts for delayed reaction-diffusion equations

Abraham Solar

This paper deals with the asymptotic behavior of solutions to the delayed monostable equation: $(*)$ $u_{t} (t, x) = u_{xx} (t, x) - u (t, x) + g (u (t - h, x)),$ $x \in R, t > 0,$ w…

math.AP2014★ 11 cited

Speed selection and stability of wavefronts for delayed monostable reaction-diffusion equations

Abraham Solar, Sergei Trofimchuk

We study the asymptotic stability of traveling fronts and front's velocity selection problem for the time-delayed monostable equation $(*)$ $u_{t}(t,x) = u_{xx}(t,x) - u(t,x) + g(u…

math.AP2014★ 12 cited

Asymptotic convergence to pushed wavefronts in a monostable equation with delayed reaction

Abraham Solar, Sergei Trofimchuk

We study the asymptotic behaviour of solutions to the delayed monostable equation $(*)$ : $u_{t} (t, x) = u_{xx} (t, x) - u (t, x) + g (u (t - h, x)),$ $x \in R, t > 0,$ with monotone reaction…