JournalsifbVol. 16, No. 2pp. 137–173

Parabolic optimal control problems on evolving surfaces subject to point-wise box constraints on the control – theory and numerical realization

  • Morten Vierling

    Universität Hamburg, Germany
Parabolic optimal control problems on evolving surfaces subject to point-wise box constraints on the control – theory and numerical realization cover
Download PDF

Abstract

We consider control-constrained linear-quadratic optimal control problems on evolving hypersurfaces in Rn+1\mathbb R^{n+1}. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of vector-valued distributions. We then carry out and prove convergence of the variational discretization of a distributed optimal control problem. In the process, we investigate the convergence of a fully discrete approximation of the state equation, and obtain optimal orders of convergence under weak regularity assumptions. We conclude with a numerical example.

Cite this article

Morten Vierling, Parabolic optimal control problems on evolving surfaces subject to point-wise box constraints on the control – theory and numerical realization. Interfaces Free Bound. 16 (2014), no. 2, pp. 137–173

DOI 10.4171/IFB/316