Optimal control for a fully parabolic singular chemotaxis model with indirect signal consumption in two space dimensions

Abstract

This paper deals with a distributed optimal control problem to a chemotaxis model with the indirect signal consumption. We first explore the global-in-time existence and uniqueness of a strong solution. Then we define the cost functional and establish the existence of the optimal solution of control problem. Finally we derive the first-order necessary optimality conditions.

Keywords:

• Singular chemotaxis
• optimal control
• global existence
• lagrange multipliers

2010 Mathematics Subject Classifications:

• 92C17
• 49J20
• 49K20
• 35K51

Acknowledgments

The authors would like to express their deep thanks to the referee's valuable suggestions for the revision and improvement of the manuscript. This work is supported by the Jilin Scientific and Technological Development Program (no. 20210101466JC).

Disclosure statement

No potential conflict of interest was reported by the author(s).