TRAVELING WAVES FOR MONOTONE SEMIFLOWS WITH WEAK COMPACTNESS

被引：166

作者：

Fang, Jian ^{[2
]}

Zhao, Xiao-Qiang ^{[1
,3
]}

机构：

[1] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

[2] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

[3] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2014年 / 46卷 / 06期

基金：

加拿大自然科学与工程研究理事会;

关键词：

monotone semiflows; traveling waves; spreading speeds; monostability; point-alpha-contraction; evolution systems; SPREADING SPEEDS; SPATIAL DYNAMICS; NONLOCAL DISPERSION; LINEAR DETERMINACY; ASYMPTOTIC SPEEDS; POPULATION-MODEL; DIFFUSION; EQUATIONS; FRONTS; SYSTEMS;

D O I：

10.1137/140953939

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the study of traveling waves for monotone semiflows of monostable type with weak compactness. To weaken the compactness condition imposed in previous works, we construct a compact set in the kinetic phase space and use an abstract variant of Helly's theorem. The obtained result is then applied to three prototypical noncompact (even non-alpha-contractive) evolution systems.

引用

页码：3678 / 3704

页数：27

共 48 条

[1]

[Anonymous], 1937, B MOSCOW U MATH MECH

[2] MULTIDIMENSIONAL NON-LINEAR DIFFUSION ARISING IN POPULATION-GENETICS [J].

ARONSON, DG ;

WEINBERGER, HF .

ADVANCES IN MATHEMATICS, 1978, 30 (01) :33-76

[3] Generalized transition waves and their properties [J].

Berestycki, Henri ;

Hamel, Francois .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2012, 65 (05) :592-648

[4] On a non-local equation arising in population dynamics [J].

Coville, Jerome ;

Dupaigne, Louis .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2007, 137 :727-755

[5] Pulsating fronts for nonlocal dispersion and KPP nonlinearity [J].

Coville, Jerome ;

Davila, Juan ;

Martinez, Salome .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2013, 30 (02) :179-223

[6]

Deimling K., 1988, NONLINEAR FUNCTIONAL

[7]

Doob J. L., 1994, Measure Theory

[8] Spatial dynamics of a nonlocal and time-delayed reaction-diffusion system [J].

Fang, Jian ;

Wei, Junjie ;

Zhao, Xiao-Qiang .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 245 (10) :2749-2770

[9] Bistable traveling waves for monotone semiflows with applications [J].

Fang, Jian ;

Zhao, Xiao-Qiang .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2015, 17 (09) :2243-2288

[10] SPATIAL DYNAMICS OF AN AGE-STRUCTURED POPULATION MODEL OF ASIAN CLAMS [J].

Fang, Jian ;

Lan, Kunquan ;

Seo, Gunog ;

Wu, Jianhong .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2014, 74 (04) :959-979

← 1 2 3 4 5 →