Generalized fronts in reaction-diffusion equations with bistable nonlinearity

被引：0

作者：

Shu, Ya Qin ^{[2
]}

Li, Wan Tong ^{[1
]}

Liu, Nai Wei ^{[3
]}

机构：

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

[2] Chongqing Univ Technol, Sch Math & Stat, Chongqing 400054, Peoples R China

[3] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2012年 / 28卷 / 08期

关键词：

Reaction-diffusion equation; transition fronts; uniqueness; bistable nonlinearity; stability; NICHOLSONS BLOWFLIES EQUATION; TRAVELING-WAVE FRONTS; EXISTENCE; STABILITY; SYSTEMS;

D O I：

10.1007/s10114-012-0015-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we first study the existence of transition fronts (generalized traveling fronts) for reaction-diffusion equations with the spatially heterogeneous bistable nonlinearity. By constructing sub-solution and super-solution we then show that transition fronts are globally exponentially stable for the solutions of the Cauchy problem. Furthermore, we prove that transition fronts are unique up to translation in time by using the monotonicity in time and the exponential decay of such transition fronts.

引用

页码：1633 / 1646

页数：14

共 33 条

[1]

Berestycki H, 2007, CONTEMP MATH, V446, P101

[2] Fronts and invasions in general domains [J].

Berestycki, Henri ;

Hamel, Francois .

COMPTES RENDUS MATHEMATIQUE, 2006, 343 (11-12) :711-716

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

Berestycki, Henri ;

Hamel, Francois .

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

[4] Bistable Traveling Waves around an Obstacle [J].

Berestycki, Henri ;

Hamel, Francois ;

Matano, Hiroshi .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2009, 62 (06) :729-788

[5]

Chen X., 1997, ADV DIFFER EQU-NY, V2, P125, DOI DOI 10.1186/1687-1847-2013-125

[6]

FIFE PC, 1977, ARCH RATION MECH AN, V65, P335, DOI 10.1007/BF00250432

[7] The wave of advance of advantageous genes [J].

Fisher, RA .

ANNALS OF EUGENICS, 1937, 7 :355-369

[8] Travelling fronts in the diffusive Nicholson's blowflies equation with distributed delays [J].

Gourley, SA .

MATHEMATICAL AND COMPUTER MODELLING, 2000, 32 (7-8) :843-853

[9] 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

[10] On the diffusive Nicholson's blowflies equation with nonlocal delay [J].

Li, W. -T. ;

Ruan, S. ;

Wang, Z. -C. .

JOURNAL OF NONLINEAR SCIENCE, 2007, 17 (06) :505-525

← 1 2 3 4 →