COMPUTATION AND STABILITY OF TRAVELING WAVES IN SECOND ORDER EVOLUTION EQUATIONS

被引：4

作者：

Beyn, W. -J. ^{[1
]}

Otten, D. ^{[1
]}

Rottmann-Matthes, J. ^{[2
]}

机构：

[1] Bielefeld Univ, Dept Math, Bielefeld, Germany

[2] Karlsruhe Inst Technol, Inst Anal, Karlsruhe, Germany

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2018年 / 56卷 / 03期

关键词：

systems of damped wave equations; traveling waves; nonlinear stability; freezing method; second order evolution equations; point spectra; essential spectra; SOLITARY WAVES; DICHOTOMIES; MODELS;

D O I：

10.1137/16M108286X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The topic of this paper is nonlinear traveling waves occuring in a system of damped wave equations in one space variable. We extend the freezing method from first to second order equations in time. When applied to a Cauchy problem, this method generates a co-moving frame in which the solution becomes stationary. In addition, it generates an algebraic variable which converges to the speed of the wave, provided the original wave satisfies certain spectral conditions and initial perturbations are sufficiently small. We develop a rigorous theory for this effect by recourse to some recent nonlinear stability results for waves in first order hyperbolic systems. Numerical computations illustrate the theory for examples of Nagumo and FitzHugh-Nagumo type.

引用

页码：1786 / 1817

页数：32