An optimal control problem of a coupled nonlinear parabolic population system

被引：0

作者：

Jia, Chao-hua ^{[1
]}

Feng, De-xing ^{[2
]}

机构：

[1] Beijing Univ Aeronaut & Astronaut, Minist Educ, LMIB, Dept Appl Math, Beijing 100083, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China

来源：

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2007年 / 23卷 / 03期

基金：

中国国家自然科学基金;

关键词：

nonlinear parabolic systems; optimal control; upper and lower solutions;

D O I：

10.1007/s10255-007-0378-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An optimal control problem for a coupled nonlinear parabolic population system is considered. The existence and uniqueness of the positive solution for the system is shown by the method of upper and lower solutions. An explicit prior bound of solutions to the system is given by considering an auxiliary coupled linear system. The existence of the optimal control is proved and the characterization of the optimal control is established.

引用

页码：377 / 388

页数：12

共 13 条

[1] Migration in age structured population dynamics [J].

Arino, O ;

Smith, WV .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 1998, 8 (05) :905-925

[2] Optimal control of a nonlinear elliptic population system [J].

Arino, O ;

Montero-Sánchez, JA .

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2000, 43 :225-241

[3] Study of an optimal control problem for diffusive nonlinear elliptic equations of logistic type [J].

Canada, A ;

Gamez, JL ;

Montero, JA .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1998, 36 (04) :1171-1189

[4] Optimal control of harvesting in a nonlinear elliptic system arising from population dynamics [J].

Cañada, A ;

Magal, P ;

Montero, JA .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 254 (02) :571-586

[5]

EVANS LC, 1998, GRAD STUD MATH AM MA, V19

[6]

Jia Chao-Hua, 2005, Acta Automatica Sinica, V31, P175

[7] Optimal control of harvesting in a parabolic system modeling two subpopulations [J].

Lenhart, SM ;

Montero, JA .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2001, 11 (07) :1129-1141

[8] OPTIMAL-CONTROL FOR ELLIPTIC VOLTERRA-LOTKA TYPE EQUATIONS [J].

LEUNG, A ;

STOJANOVIC, S .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 173 (02) :603-619

[9]

Leung A., 1989, SYSTEMS NONLINEAR PA

[10] Mathematical modelling of macrophage dynamics in tumours [J].

Owen, MR ;

Sherratt, JA .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 1999, 9 (04) :513-539

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