Evans function and blow-u[ methods in critical eienvalue problems
Evans function and blow-u[ methods in critical eienvalue problems
复制标题
临界特征值问题中的埃文斯函数和blow-u[方法
DOI：
10.3934/dcds.2004.10.941
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
A. Scheel
中科院分区：
文献类型：
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作者：
Bjorn Sandstede;A. Scheel
接触缺陷是由反应扩散系统模拟的振荡介质中常见的几种缺陷之一。这些缺陷的一个有趣的性质是，渐近的空间波数仅以代数阶O(1/x)逼近(相关的相位对数发散)。接触缺陷的偏微分方程线性化的本质谱总是在原点有一个分支点。我们证明了Evans函数可以在这个分支点上扩张，并讨论了扩张的光滑性。该建筑采用了爆炸技术，性质相当一般。我们还评论了Evans函数的根与Green函数的时间渐近性之间的已知关系，并讨论了它在代数衰变孤子中的应用。
Contact defects are one of several types of defects that arise generically in oscillatory media modelled by reaction-diffusionsystems. An interesting property of these defects is that the asymptotic spatial wave number is approached only with algebraic order O(1/x) (the associated phase diverges logarithmically). The essential spectrum of the PDE linearization about a contact defect always has a branch point at the origin. We show that the Evans function can be extended across this branch point and discuss the smoothness properties of the extension. The construction utilizes blow-up techniques and is quite general in nature. We also comment on known relations between roots of the Evans function and the temporal asymptotics of Green’s functions, and discuss applications to algebraically decaying solitons.