Existence of Traveling Waves of General Gray-Scott Models

被引：2

作者：

Zheng, Zhi ^{[1
]}

Chen, Xinfu ^{[2
]}

Qi, Yuanwei ^{[3
]}

Zhou, Shulin ^{[4
]}

机构：

[1] Peking Univ, Sch Math, Beijing 100871, Peoples R China

[2] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

[3] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

[4] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2018年 / 30卷 / 04期

基金：

中国国家自然科学基金;

关键词：

General Gray-Scott model; Traveling wave; Existence; Bounded speed set; REACTION-DIFFUSION SYSTEMS; ISOTHERMAL CHEMICAL-SYSTEM; QUADRATIC AUTOCATALYSIS; CRITICAL NONLINEARITY; SPIKE AUTOSOLITONS; STABILITY ANALYSIS; PATTERN-FORMATION; SELF-SIMILARITY; STEADY-STATES; SIR MODEL;

D O I：

10.1007/s10884-017-9603-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work gives a rigorous proof of the existence of propagating traveling waves of a nonlinear reaction-diffusion system which is a general Gray-Scott model of the premixed isothermal autocatalytic chemical reaction of order m (m > 1) between two chemical species, a reactant A and an auto-catalyst B, A+ mB. (m + 1) B, and a super-linear decay of order n > 1, B. C, where 1 < n < m. Here C is an inert product. Moreover, we establish that the speed set for existence must lie in a bounded interval for a given initial value u0 at -8. The explicit bound is also derived in terms of u0 and other parameters. The same system also appears in a mathematical model of SIR type in infectious diseases.

引用

页码：1469 / 1487

页数：19

共 46 条

[1] MULTIDIMENSIONAL NON-LINEAR DIFFUSION ARISING IN POPULATION-GENETICS
ARONSON, DG
WEINBERGER, HF
[J]. ADVANCES IN MATHEMATICS, 1978, 30 (01) : 33 - 76
[2] Traveling waves in a convolution model for phase transitions
Bates, PW
Fife, PC
Ren, XF
Wang, XF
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1997, 138 (02) : 105 - 136
[3] Traveling waves of bistable dynamics on a lattice
Bates, PW
Chen, XF
Chmaj, AJJ
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2003, 35 (02) : 520 - 546
[4] Global large time self-similarity of a thermal-diffusive combustion system with critical nonlinearity
Bricmont, J
Kupiainen, A
Xin, J
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 130 (01) : 9 - 35
[5] Chen X., MULTIPLE TRAVELING W
[6] Propagation of Local Disturbances in Reaction Diffusion Systems Modeling Quadratic Autocatalysis
Chen, Xinfu
Qi, Yuanwei
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2008, 69 (01) : 273 - 282
[7] Sharp estimates on minimum travelling wave speed of reaction diffusion systems modelling autocatalysis
Chen, Xinfu
Qi, Yuanwei
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2007, 39 (02) : 437 - 448
[8] Existence of traveling waves of auto-catalytic systems with decay
Chen, Xinfu
Qi, Yuanwei
Zhang, Yajing
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (11) : 7982 - 7999
[9] Cuo JS, 2009, Q APPL MATH, V67, P559
[10] Semistrong pulse interactions in a class of coupled reaction-diffusion equations
Doelman, A
Kaper, TJ
[J]. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2003, 2 (01): : 53 - 96

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