Traveling waves for Nonlocal and Non-monotone Delayed Reaction-diffusion Equations

被引：6

作者：

Xu, Zhi Ting ^{[1
]}

Weng, Pei Xuan ^{[1
]}

机构：

[1] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2013年 / 29卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Nonlocal; non-monotone; delayed reaction-diffusion equation; traveling wave solutions; auxiliary equation; VECTOR-DISEASE-MODEL; DIFFERENTIAL-EQUATIONS; SPATIOTEMPORAL DELAYS; POPULATION-MODEL; FRONTS; SYSTEMS; EXISTENCE; STABILITY; SPREAD; SPEEDS;

D O I：

10.1007/s10114-013-1769-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the existence of traveling wave solutions for a nonlocal and non-monotone delayed reaction-diffusion equation. Based on the construction of two associated auxiliary reaction diffusion equations with monotonicity and by using the traveling wavefronts of the auxiliary equations, the existence of the positive traveling wave solutions for c >= c(*) is obtained. Also, the exponential asymptotic behavior in the negative infinity was established. Moreover, we apply our results to some reaction-diffusion equations with spatio-temporal delay to obtain the existence of traveling waves. These results cover, complement and/or improve some existing ones in the literature.

引用

页码：2159 / 2180

页数：22

共 26 条

[1] DETERMINISTIC EPIDEMIC WAVES OF CRITICAL VELOCITY [J].

BROWN, KJ ;

CARR, J .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1977, 81 (MAY) :431-433

[2] Existence and uniqueness of traveling waves for non-monotone integral equations with applications [J].

Fang, Jian ;

Zhao, Xiao-Qiang .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (09) :2199-2226

[3] Travelling waves for delayed reaction-diffusion equations with global response [J].

Faria, T ;

Huang, W ;

Wu, JH .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2006, 462 (2065) :229-261

[4] Nonmonotone travelling waves in a single species reaction-diffusion equation with delay [J].

Faria, Teresa ;

Trofimchuk, Sergei .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 228 (01) :357-376

[5] GEOMETRIC SINGULAR PERTURBATION-THEORY FOR ORDINARY DIFFERENTIAL-EQUATIONS [J].

FENICHEL, N .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1979, 31 (01) :53-98

[6]

Gourley SA, 2006, FIELDS I COMMUN, V48, P137

[7] Wavefronts and global stability in a time-delayed population model with stage structure [J].

Gourley, SA ;

Kuang, Y .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2003, 459 (2034) :1563-1579

[8] SPREADING SPEEDS AND TRAVELING WAVES FOR NONMONOTONE INTEGRODIFFERENCE EQUATIONS [J].

Hsu, Sze-Bi ;

Zhao, Xiao-Qiang .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2008, 40 (02) :776-789

[9] Existence of traveling wavefronts of delayed reaction diffusion systems without monotonicity [J].

Huang, JH ;

Zou, XF .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2003, 9 (04) :925-936

[10] Existence of traveling waves for integral recursions with nonmonotone growth functions [J].

Li, Bingtuan ;

Lewis, Mark A. ;

Weinberger, Hans F. .

JOURNAL OF MATHEMATICAL BIOLOGY, 2009, 58 (03) :323-338

← 1 2 3 →