有關無窮維度差分方程系統全解之研究

Abstract

我們將研究無窮維度差分方程系統之全解的存在性問題，在此所考慮的系統是反應擴散方程的離散型。此類系統常見於許多應用上，例如影像處理、材料科學等。我們主要興趣在Fisher、Nagumo、Zeldovich 及m 次 Fisher 等不同的反應項。

We shall study the existence of entire solutions for infinite dimensional systems of difference equations ( so-called coupled map lattices), which is discretized systems of some reaction-diffusion equations. Such systems arise in many applications, such as image processing, material science.We are mainly interested in Fisher’s type, Nagumo’s type, Zeldovich’s type, and the m-th Fisher’s type.