Stability of Traveling Waves in Partly Parabolic Systems

被引：9

作者：

Ghazaryan, A. ^{[1
]}

Latushkin, Y. ^{[2
]}

Schecter, S. ^{[3
]}

机构：

[1] Miami Univ, Dept Math, Oxford, OH 45056 USA

[2] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[3] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

来源：

MATHEMATICAL MODELLING OF NATURAL PHENOMENA | 2013年 / 8卷 / 05期

基金：

美国国家科学基金会;

关键词：

traveling wave; spectral stability; linear stability; nonlinear stability; exponential weights; REACTION-DIFFUSION SYSTEMS; TWISTED HETEROCLINIC LOOP; FITZHUGH-NAGUMO EQUATIONS; NUMBER COMBUSTION FRONTS; CALCIUM WAVES; INVARIANT FOLIATIONS; IMMOBILE BUFFERS; CENTER MANIFOLDS; POROUS-MEDIA; DYNAMICS;

D O I：

10.1051/mmnp/20138503

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We review recent results on stability of traveling waves in partly parabolic reaction-diffusion systems with stable or marginally stable equilibria. We explain how attention to what are apparently mathematical technicalities has led to theorems that allow one to convert spectral calculations, which are used in the sciences and engineering to study stability of a wave, into detailed, theoretically-based information about the behavior of perturbations of the wave.

引用

页码：31 / 47

页数：17

共 69 条

[11]

Briggs R., 1964, Electron-Stream Interaction with Plasmas

[12] CONVERGENCE TO EQUILIBRIUM STATES FOR A REACTION-DIFFUSION SYSTEM MODELING THE SPATIAL SPREAD OF A CLASS OF BACTERIAL AND VIRAL DISEASES [J].