# American Institute of Mathematical Sciences

September  2017, 7(3): 325-344. doi: 10.3934/naco.2017021

## Analysis of optimal boundary control for a three-dimensional reaction-diffusion system

 1 Zhuhai College of Jilin University, Zhuhai, China 2 School of Science, Curtin University, Australia 3 Department of Mathematics and Statistics, Curtin University, Australia 4 School of Business, National University of Singapore, Singapore 5 Business School, Nankai University, Tianjin, China

* Corresponding author

The reviewing process of the paper was handled by Shengjie Li as Guest Editor

Received  April 2016 Revised  May 2017 Published  July 2017

Fund Project: This work is partially supported by Australian Research Council Grant DP160102189 and by a grant from Curtin University, Australia.

This paper is concerned with optimal boundary control of a three dimensional reaction-diffusion system in a more general form than what has been presented in the literature. The state equations are analyzed and the optimal control problem is investigated. Necessary and sufficient optimality conditions are derived. The model is widely applicable due to its generality. Some examples in applications are discussed.

Citation: Wanli Yang, Jie Sun, Su Zhang. Analysis of optimal boundary control for a three-dimensional reaction-diffusion system. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 325-344. doi: 10.3934/naco.2017021
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