Identifications Of Parameters In Parabolic Systems

In this paper, we consider identifications of physical parameters in the following parabolic initial-boundary value problems.The identification problem is formulated as a constrained minimization problem by using the output least squares approach with the H1-regularization. By intro-ducing a penalty function as the following, for every e > 0,we construct a sequence of unconstrained minimization problems to approximate the constrained minimization problem. The solutions of such a sequence of unconstrained minimization problems all exist, and they converge to the solution of the constrained minimization problem in a certain sense. In this paper, the following results are approached,Theorem 3.1 The problem (P) has at least one solution.Theorem 3.2 For every e > 0, let (q, v) be the solution to the problem (P), then there is a subsequence of {(q, u)}, still denoted by itself, and some v* with q*, such thatMoreover , (q*,v*) is the optimal solution to the problem (P).Theorem 3.3 Let (q,v) be the optimal solution to the problem (P) satisfying when → 0, q→q*, v→v* in the sense of Theorem 3.2, where (q*,v*) is the optimal solution to the problem (P), then there is a subsequence of {J(q, v)}, still denoted by itself, such that...