Traveling waves in a bio-reactor model with stage-structure

被引：25

作者：

Wang, Zhi-Cheng ^{[1
,2
]}

Wu, Jianhua ^{[2
]}

机构：

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

[2] Shaanxi Normal Univ, Coll Math & Informat Sci, Xian 710062, Shaanxi, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 385卷 / 02期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Bio-reactor model; Traveling wave solutions; Stage-structure; Fixed point theorem; EPIDEMIC MODEL; CHEMOSTAT; SPREAD;

D O I：

10.1016/j.jmaa.2011.06.084

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper the existence and non-existence of traveling wave solutions are established for a bio-reactor model with stage-structure. The method to prove the existence of wave solutions is to construct an invariant cone of initial functions defined in a large but bounded domain, to apply a fixed point theorem on this cone and then extend to the unbounded spatial domain R by a limiting argument. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：683 / 692

页数：10

共 22 条

[1]

Ballyk M, 1998, SIAM J APPL MATH, V59, P573

[2] Instability in diffusive ecological models with nonlocal delay effects [J].

Boushaba, K ;

Ruan, S .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 258 (01) :269-286

[3] Travelling wave solutions for an infection-age structured model with diffusion [J].

Ducrot, A. ;

Magal, P. .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2009, 139 :459-482

[4] Travelling Wave Solutions in Multigroup Age-Structured Epidemic Models [J].

Ducrot, Arnaut ;

Magal, Pierre ;

Ruan, Shigui .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 195 (01) :311-331

[5]

GILBARG D., 2000, Elliptic Partial Differential Equations of Second Order, V2nd

[6] Global stability in chemostat-type plankton models with delayed nutrient recycling [J].

He, XZ ;

Ruan, SG .

JOURNAL OF MATHEMATICAL BIOLOGY, 1998, 37 (03) :253-271

[7] DIFFERENTIAL-EQUATION MODELS OF SOME PARASITIC INFECTIONS - METHODS FOR THE STUDY OF ASYMPTOTIC-BEHAVIOR [J].

HIRSCH, WM ;

HANISCH, H ;

GABRIEL, JP .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1985, 38 (06) :733-753

[8] TRAVELING WAVES FOR A SIMPLE DIFFUSIVE EPIDEMIC MODEL [J].

HOSONO, Y ;

ILYAS, B .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 1995, 5 (07) :935-966

[9]

Huang W., 2004, J. of Dynamics and DifF. Eq, V16, P745, DOI DOI 10.1007/s10884-004-6115-x

[10] A SIMPLE-MODEL FOR THE SPATIAL SPREAD AND CONTROL OF RABIES [J].

KALLEN, A ;

ARCURI, P ;

MURRAY, JD .

JOURNAL OF THEORETICAL BIOLOGY, 1985, 116 (03) :377-393

← 1 2 3 →