Ze-Rong He, Nan Zhou
Abstract:
This article concerns the approximate controllability of a biological system,
which is composed of two hierarchical age-structured competing species.
Basing on a controllability result of linear system, we prove that the nonlinear
system is approximately controllable by means of a fixed point theorem for
multi-valued mappings. To fix a suitable control policy, we deal with an
optimal control problem and established the existence of the unique optimal strategy.
In addition, the stabilization problem of the system is also considered.
Submitted November 19, 2019. Published June 11, 2020.
Math Subject Classifications: 92D05, 47D06, 35B35.
Key Words: Hierarchy of age; population system; competition; controllability;
Fan-Glicksberg fixed points.
DOI: 10.58997/ejde.2020.58
Show me the PDF file (315 KB), TEX file for this article.
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Ze-Rong He Department of Mathematics Institute of Operational Research and Cybernetics Hangzhou Dianzi University Hangzhou 310018, China email: zrhe@hdu.edu.cn |
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Nan Zhou Department of Mathematics Institute of Operational Research and Cybernetics Hangzhou Dianzi University Hangzhou 310018, China email: 1749521930@qq.com |
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