Optimal Control and Asymptotic Analysis of the Cattaneo Equation

Abstract

We compare the classical Fourier model for heat transfer to the Cattaneo model for delayed heat transfer. In particular, we consider the asymptotic behavior of the Cattaneo model for a vanishing delay time in the context of an optimal control problem with tracking type cost functional. It is possible to rigorously prove that both optimal controls and states for this problem constrained by the Cattaneo equation converge to the respective optimal control and state of the problem constrained by the heat equation (cf.[1]). Here, we present a short overview of the topic as well as some numerical results for the limit process.