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Palabras claves o descriptores: NONLOCAL DELAY (Comienzo)
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Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Wang, Zhi-Cheng ; Ruan, Shigui ; Li, Wan-Tong
Título: Entire solutions in bistable reaction-diffusion equations with nonlocal delayed nonlinearity
Páginas/Colación: pp. 2047-2084
Fecha: Apil 2009
Transactions of the American Mathematical Society Vol. 361, no.4 April 2009
Información de existenciaInformación de existencia

Palabras Claves: Palabras: BISTABLE NONLINEARITY BISTABLE NONLINEARITY, Palabras: ENTIRE SOLUTION ENTIRE SOLUTION, Palabras: NONLOCAL DELAY NONLOCAL DELAY, Palabras: TRAVELING WAVE SOLUTION TRAVELING WAVE SOLUTION

Resumen
This paper is concerned with entire solutions for bistable reaction-diffusion equations with nonlocal delay in one-dimensional spatial domain

This paper is concerned with entire solutions for bistable reaction-diffusion equations with nonlocal delay in one-dimensional spatial domain. Here the entire solutions are defined in the whole space and for all time $ t\in \mathbb{R}$. Assuming that the equation has an increasing traveling wave solution with nonzero wave speed and using the comparison argument, we prove the existence of entire solutions which behave as two traveling wave solutions coming from both ends of the $ x$-axis and annihilating at a finite time. Furthermore, we show that such an entire solution is unique up to space-time translations and is Liapunov stable. A key idea is to characterize the asymptotic behavior of the solutions as $ t\to -\infty$in terms of appropriate subsolutions and supersolutions. In order to illustrate our main results, two models of reaction-diffusion equations with nonlocal delay arising from mathematical biology are considered.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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