Volume 11, Issue 4
Optimal Control Problem for a Reaction-Diffusion System of Three Populations

Xiaoni Wang, Gaihui Guo & Jian Li

East Asian J. Appl. Math., 11 (2021), pp. 808-828.

Published online: 2021-08

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  • Abstract

The work deals with an optimal control problem for a reaction-diffusion system comprising two competing populations, one of which is a prey for a third population. In order to maximise the total density of these populations, the existence and uniqueness of a positive strong solution of a controlled system are studied. After that, the techniques of minimal sequences is used in order to show the existence of an optimal solution. The first and second order optimality conditions are also constructed.

  • Keywords

Optimal control, reaction-diffusion, controlled system, optimality conditions.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-11-808, author = {Xiaoni and Wang and and 17770 and and Xiaoni Wang and Gaihui and Guo and and 17771 and and Gaihui Guo and Jian and Li and and 17773 and and Jian Li}, title = {Optimal Control Problem for a Reaction-Diffusion System of Three Populations}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {11}, number = {4}, pages = {808--828}, abstract = {

The work deals with an optimal control problem for a reaction-diffusion system comprising two competing populations, one of which is a prey for a third population. In order to maximise the total density of these populations, the existence and uniqueness of a positive strong solution of a controlled system are studied. After that, the techniques of minimal sequences is used in order to show the existence of an optimal solution. The first and second order optimality conditions are also constructed.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.281020.290421}, url = {http://global-sci.org/intro/article_detail/eajam/19373.html} }
TY - JOUR T1 - Optimal Control Problem for a Reaction-Diffusion System of Three Populations AU - Wang , Xiaoni AU - Guo , Gaihui AU - Li , Jian JO - East Asian Journal on Applied Mathematics VL - 4 SP - 808 EP - 828 PY - 2021 DA - 2021/08 SN - 11 DO - http://doi.org/10.4208/eajam.281020.290421 UR - https://global-sci.org/intro/article_detail/eajam/19373.html KW - Optimal control, reaction-diffusion, controlled system, optimality conditions. AB -

The work deals with an optimal control problem for a reaction-diffusion system comprising two competing populations, one of which is a prey for a third population. In order to maximise the total density of these populations, the existence and uniqueness of a positive strong solution of a controlled system are studied. After that, the techniques of minimal sequences is used in order to show the existence of an optimal solution. The first and second order optimality conditions are also constructed.

Xiaoni Wang, Gaihui Guo & Jian Li. (2021). Optimal Control Problem for a Reaction-Diffusion System of Three Populations. East Asian Journal on Applied Mathematics. 11 (4). 808-828. doi:10.4208/eajam.281020.290421
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