Layers and spikes in non-homogeneous bistable reaction-diffusion equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Layers and spikes in non-homogeneous bistable reaction-diffusion equations

Authors:	Shangbing Ai Xinfu Chen Stuart P Hastings

Institution:	Department of Mathematical Sciences, University of Alabama at Huntsville, Huntsville, Alabama 35899 ; Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 ; Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

Abstract:	We study $\varepsilon^2\ddot{u}=f(u,x)=A\, u\, (1-u)\,(\phi-u)$ , where , $\phi=\phi(x)\in(0,1)$ , and $\varepsilon>0$ is sufficiently small, on an interval with boundary conditions $\dot{u}=0$ at . All solutions with an $\varepsilon$ independent number of oscillations are analyzed. Existence of complicated patterns of layers and spikes is proved, and their Morse index is determined. It is observed that the results extend to $f=A(u,x) (u-\phi_-)\,(u-\phi)\,(u-\phi_+)$ with $\phi_-(x)<\phi(x)<\phi_+(x)$ and also to an infinite interval.

Keywords:

	点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文