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pro vyhledávání: '"Solar, Abraham"'
Autor:
Solar, Abraham, Trofimchuk, Sergei
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 monostable traveling waves. Our approach allows to compute, in the moving
Externí odkaz:
http://arxiv.org/abs/2107.11938
Akademický článek
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Autor:
Solar, Abraham
This paper deals with the stability of semi-wavefronts to the following delay non-local monostable equation: $\dot{v}(t,x) = \Delta v(t,x) - v(t,x) + \int_{\R^d}K(y)g(v(t-h,x-y))dy, x \in \R^d,\ t >0;$ where $h>0$ and $d\in\Z_+$. We give two general
Externí odkaz:
http://arxiv.org/abs/1808.07200
Autor:
Solar, Abraham, Trofimchuk, Sergei
Publikováno v:
Journal of Differential Equations 266 (2019) pp. 6647-6660
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 an open problem concerning the uniqueness of non-monotone (hence, slowl
Externí odkaz:
http://arxiv.org/abs/1808.04857
Autor:
D., Rafael Benguria, Solar, Abraham
We give an iterative method to estimate the disturbance of semi-wavefronts of the equation: $\dot{u}(t,x) = u''(t,x) +u(t,x)(1-u(t-h,x)),$ $x \in \mathbb{R},\ t >0;$ where $h>0.$ As a consequence, we show the exponential stability, with an unbounded
Externí odkaz:
http://arxiv.org/abs/1806.04255
Autor:
Benguria, Rafael, Solar, Abraham
We study the large time asymptotic behavior of the solutions of the linear parabolic equation with delay $(*)$: $u_{t}(t,x) = u_{xx}(t,x) - u(t,x) + \int_{\mathbb{R}} k(x-y) \, u (t-h, y)\, dy$, $x \in \R$, $\ t >0$, and $k(x) \in L^1(\R)$. As an app
Externí odkaz:
http://arxiv.org/abs/1801.06151
Autor:
Solar, Abraham
This paper deals with the asymptotic behavior of solutions to the delayed monostable equation: $(*)$ $u_{t}(t,x) = u_{xx}(t,x) - u(t,x) + g(u(t-h,x)),$ $x \in \mathbb{R},\ t >0,$ where $h>0$ and the reaction term $g: \mathbb{R}_+ \to \mathbb{R}_+$ ha
Externí odkaz:
http://arxiv.org/abs/1704.03011
Autor:
Solar, Abraham, Trofimchuk, Sergei
Publikováno v:
Journal of Dynamics and Differential Equations 28 (2016) 1265-1292
We study the asymptotic stability of traveling fronts and front's velocity selection problem for the time-delayed monostable equation $(*)$ $u_{t}(t,x) = u_{xx}(t,x) - u(t,x) + g(u(t-h,x)),\ x \in \mathbb{R},\ t >0$, considered with Lipschitz continu
Externí odkaz:
http://arxiv.org/abs/1412.3129
Autor:
Solar, Abraham, Trofimchuk, Sergei
Publikováno v:
Nonlinearity 28 (2015) 2027-2052
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 term $g: R_+ \to R_+$. Our basic assumption is that this equation pos
Externí odkaz:
http://arxiv.org/abs/1408.3344
Autor:
Solar, Abraham, Trofimchuk, Sergei
Publikováno v:
In Journal of Differential Equations 5 May 2019 266(10):6647-6660