A note on a nonlocal nonlinear reaction-diffusion model

被引：4

作者：

Walker, Christoph ^{[1
]}

机构：

[1] Leibniz Univ Hannover, Inst Angew Math, D-30167 Hannover, Germany

来源：

APPLIED MATHEMATICS LETTERS | 2012年 / 25卷 / 11期

关键词：

Bifurcation; Steady states; Cross-diffusion; Age structure; Maximal regularity; PREY-PREDATOR SYSTEM; POSITIVE SOLUTIONS; GLOBAL BIFURCATION; CROSS-DIFFUSION; EQUATIONS;

D O I：

10.1016/j.aml.2012.02.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give an application of the Crandall-Rabinowitz theorem on local bifurcation to a system of nonlinear parabolic equations with nonlocal reaction and cross-diffusion terms as well as nonlocal initial conditions. The system arises as steady-state equations of two interacting age-structured populations. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：1772 / 1777

页数：6

共 18 条

[1] FIXED-POINT EQUATIONS AND NONLINEAR EIGENVALUE PROBLEMS IN ORDERED BANACH-SPACES [J].

AMANN, H .

SIAM REVIEW, 1976, 18 (04) :620-709

[2]

[Anonymous], 1992, PITMAN RES NOTES MAT

[3]

[Anonymous], 1995, ABSTRACT LINEAR THEO

[4] GLOBAL BIFURCATION OF POSITIVE SOLUTIONS IN SOME SYSTEMS OF ELLIPTIC-EQUATIONS [J].

BLAT, J ;

BROWN, KJ .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1986, 17 (06) :1339-1353

[5]

Crandall M.G., 1971, J. Funct. Anal., V8, P321, DOI DOI 10.1016/0022-1236(71)90015-2

[6] ON POSITIVE SOLUTIONS OF SOME PAIRS OF DIFFERENTIAL-EQUATIONS [J].

DANCER, EN .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 284 (02) :729-743

[7] On the symbiotic Lotka-Volterra model with diffusion and transport effects [J].

Delgado, M ;

López-Gómez, J ;

Suárez, A .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 160 (01) :175-262

[8] Nonlinear age-dependent diffusive equations:: A bifurcation approach [J].

Delgado, Manuel ;

Molina-Becerra, Monica ;

Suarez, Antonio .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 244 (09) :2133-2155

[9] Stability of steady-state solutions to a prey-predator system with cross-diffusion [J].

Kuto, K .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 197 (02) :293-314

[10] Multiple coexistence states for a prey-predator system with cross-diffusion [J].

Kuto, K ;

Yamada, Y .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 197 (02) :315-348

← 1 2 →