一类积微分方程组解界面的产生

Generation of Interfaces in a Class of Integrodifferential Equations

研究含小参数 ε的积微分方程组εuεt-Jε* uε+uε=f ( uε,vε) =F( uε) -vε,vεt-DΔvε =uε -γvε界面的产生 。

This paper is concerned with the emergence of transition layers in the following integrodifferential equations:εu ε t-J ε*u ε+u ε=f(u ε,v ε)=F(u ε)-v ε, v ε t-DΔv ε=u ε-γv ε,where D>0,γ>0 are constants; 0<ε1 is a small parameter; F′(u)=0 has just two roots a -<a +, with F(a -)<0<F(a +); and J ε is a convolution operator with the kernel J ε(x)=ε -1J(x/ε) satisfying some conditions. A precise estimate on the width of the transition layer and the length of time for the layer generation have been established.