A General Approach for Front-Propagation in Functional Reaction-Diffusion Equations

被引：4

作者：

Calamai, Alessandro ^{[1
]}

Marcelli, Cristina ^{[1
]}

Papalini, Francesca ^{[1
]}

机构：

[1] Univ Politecn Marche, Dipartimento Sci Matemat, I-60131 Ancona, Italy

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2009年 / 21卷 / 04期

关键词：

Delayed reaction-diffusion equations; Non-local reaction-diffusion equations; Traveling waves; Monostable reaction-term; Upper and lower-solutions method; Fixed point; TRAVELING WAVE-FRONTS; EXISTENCE; SYSTEMS;

D O I：

10.1007/s10884-009-9153-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the persistence of front propagation for functional reaction-diffusion equations v(tau) = v(xx) + F(v) where F is a given operator. By combining the upper and lower solution method with fixed point techniques, we prove a general existence theorem for traveling waves. Our result applies to reaction-diffusion equation with delayed or non-local reaction term.

引用

页码：567 / 593

页数：27

共 18 条

[1]

[Anonymous], ACTA MATH APPL SIN-E

[2]

[Anonymous], 1979, LECT NOTES BIOMATHEM

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

ARONSON, DG ;

WEINBERGER, HF .

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

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

Fisher, RA .

ANNALS OF EUGENICS, 1937, 7 :355-369

[6]

Gilding BH., 2004, Travelling Waves in Nonlinear Diffusion-Convection Reaction

[7] Travelling front solutions of a nonlocal Fisher equation [J].

Gourley, SA .

JOURNAL OF MATHEMATICAL BIOLOGY, 2000, 41 (03) :272-284

[8] 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

[9] Traveling Wave Fronts of Reaction-Diffusion Systems with Delay [J].

Jianhong Wu ;

Xingfu Zou .

Journal of Dynamics and Differential Equations, 2001, 13 (3) :651-687

[10]

KAMIN S, 2004, ATTI ACCAD NAZ LINCE, V15, P271

← 1 2 →