SOLVING A PARABOLIC IDENTIFICATION PROBLEM BY OPTIMAL CONTROL METHODS HEM RAJ JOSHI AND SUZANNE LENHART

Abstract. An unknown coefficient of the interaction term of a parabolic system with a Neumann boundary condition in a multi-dimensional bounded domain is identified. The solution of the system represents the concentra-tions of prey and predator populations. Given partial (perhaps noisy) ob-servations of a true solution in a subdomain, we seek to “identify ” the coef-ficient of the interaction term using an optimal control technique, involving Tikhonov’s regularization. The existence and uniqueness of the optimal con-trol approximating the desired coefficient are obtained, an optimality system is derived, the identification problem is discussed and an example illustrating how to find a solution numerically is presented. 1