Identification of the Interaction Coefficients in an Intraspecific Competition Model with Diffusion Terms

Abstract

In this paper, we are interested in identifying the coefficients of the interaction terms in a parabolic system, which describes two subpopulations of the same species competing for the same resources. We use optimal the control theory to study the identification problem. Taking the unknown coefficients as control functions, the identification problem is transformed into an optimal control problem. We prove the existence and local uniqueness of the optimal control, derive the first-order necessary condition, and get the formula of the optimal control.