IDENTIFICATION FOR PARABOLIC DISTRIBUTED PARAMETER SYSTEMS WITH CONSTRAINTS ON THE PARAMETERS AND THE STATE

摘要

We consider the problems for identifying the parameters a(11)(x, t),...,a(mm)(x, t) and c(x, t) involved in a second-order, linear, uniformly parabolic equation partial derivative(t)u - partial derivative(i)(a(ij) (x, t)partial derivative(j)u) + bi(x, t)partial derivative(i)u + c(x, t)u = f(x, t) in Omega x (0, T), u(partial derivative Omega) = g, u(t = 0) = u(0)(x), x is an element of Omega. on the basis of noisy measurement data z(x) = u(x, T) + w(x), x is an element of Omega with equality and inequality constraints on the parameters and the state variable. The cost functionals are (one-sided) Gateaux-differentiable with respect to the state variables and the parameters. Using the Duboviskii-Miljutin lemma we get the two maximum principles for the two identification problems, respectively, i.e., the necessary conditions for the existence of optimal parameters. [References: 29]