GLOBAL STABILITY OF V-SHAPED TRAVELING FRONTS IN COMBUSTION AND DEGENERATE MONOSTABLE EQUATIONS

被引：18
作者：
Bu, Zhen-Hui [1 ]
Wang, Zhi-Cheng [1 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 05期
关键词：
V-shaped traveling front; combustion nonlinearity; degenerate monostable nonlinearity; stability; reaction-diffusion equation; REACTION-DIFFUSION EQUATIONS; FISHER-KPP EQUATION; CURVED FRONTS; PYRAMIDAL SHAPES; EXISTENCE; WAVES; MODEL; UNIQUENESS;
D O I：
10.3934/dcds.2018093
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with the global stability of V-shaped traveling fronts in reaction-diffusion equations with combustion and degenerate monostable nonlinearity. The existence of such curved fronts has been recently proved by [39]. In this paper, by constructing new subsolutions, we show the asymptotic stability of V-shaped traveling fronts.
引用
收藏
页码：2251 / 2286
页数：36
相关论文
共 43 条
[1]  
[Anonymous], 1979, LECT NOTES BIOMATHEM
[2]   MULTIDIMENSIONAL NON-LINEAR DIFFUSION ARISING IN POPULATION-GENETICS [J].
ARONSON, DG ;
WEINBERGER, HF .
ADVANCES IN MATHEMATICS, 1978, 30 (01) :33-76
[3]   Existence of nonplanar solutions of a simple model of premixed Bunsen flames [J].
Bonnet, A ;
Hamel, F .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1999, 31 (01) :80-118
[4]   Exact solutions for the kinematic model of autowaves in two-dimensional excitable media [J].
Brazhnik, PK .
PHYSICA D, 1996, 94 (04) :205-220
[5]   STABILITY OF PYRAMIDAL TRAVELING FRONTS IN THE DEGENERATE MONOSTABLE AND COMBUSTION EQUATIONS I [J].
Bu, Zhen-Hui ;
Wang, Zhi-Cheng .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (05) :2395-2430
[6]   CURVED FRONTS OF MONOSTABLE REACTION-ADVECTION-DIFFUSION EQUATIONS IN SPACE-TIME PERIODIC MEDIA [J].
Bu, Zhen-Hui ;
Wang, Zhi-Cheng .
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2016, 15 (01) :139-160
[7]   AN APPLICATION OF THE GENERALIZED MORSE INDEX TO TRAVELING WAVE SOLUTIONS OF A COMPETITIVE REACTION-DIFFUSION MODEL [J].
CONLEY, C ;
GARDNER, R .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1984, 33 (03) :319-343
[8]   Two-dimensional curved fronts in a periodic shear flow [J].
El Smaily, Mohammad ;
Hamel, Francois ;
Huang, Rui .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (17) :6469-6486
[9]  
FIFE PC, 1981, ARCH RATION MECH AN, V75, P281
[10]  
FIFE PC, 1977, ARCH RATION MECH AN, V65, P335, DOI 10.1007/BF00250432
12345