Parameter Estimations in Nonlinear Parabolic Systems with Time Delay

摘要

In the present paper we consider a parameter identification problem associated with systems governed by nonlinear parabolic partial differential equations with delays. To be precise, a distributed parameter model describing spatially-dependent hepatic processing of the chemical compound named dioxin or TCDD is analysed. The associated inverse problem is formulated in an operator theoretic setting for a least squares optimization problem. Galerkin type approximations are used to define a family of approximate optimization problems. Finally, the convergence result of the parameter identification problem is tested numerically, using both exact and noisy data.