1Department of Mathematics, Central University of Tamil Nadu, Thiruvarur610 005, India
4Department of Applied Sciences, National Institute of Technology Goa, Goa403 401, India
*E-mail: *navennkrrish@gmail.com
The paper studies the optimal control problem of a three-competition Lotka-Volterra reaction-diffusion system. We begin by proving the existence and uniqueness of a weak solution of the controlled system using Galerkin method which is then followed by the existence of the optimal pair for the corresponding optimal control problem. Further, we verify the differentiability of the control-to-state operator V and derive the necessary optimality condition for the control problem.
2010 Mathematics Subject Classification: 35K40, 49K20.
Optimal control, Fréchet gradient, Lotka-Volterra model
