離散型反應擴散方程的全解

Abstract

這篇文章中，我們探討離散型反應擴散方程u_t(x,t)=u(x+1,t)-2u(x,t)+u(x-1,t)+f(u(x,t))，其中\n反應項f(u)=u^2(1-u)。在此，\n我們證明此方程式存在一種全解其動態行為宛如兩個來自x軸兩端相向而行的行波。

This paper deals with a discrete reaction-diffusion equation\nu_t(x,t)=u(x+1,t)-2u(x,t)+u(x-1,t)+f(u(x,t)),\nwhere f(u)=u^2(1-u). Here, we prove there exist entire solutions which behave as two\ntraveling waves coming from both sides of x-axis.