Control-constrained parabolic optimal control problems on evolving surfaces - theory and variational discretization
Optimization and Control
2015-03-19 v4 Systems and Control
Analysis of PDEs
Numerical Analysis
Abstract
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. 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
@article{arxiv.1106.0622,
title = {Control-constrained parabolic optimal control problems on evolving surfaces - theory and variational discretization},
author = {Morten Vierling},
journal= {arXiv preprint arXiv:1106.0622},
year = {2015}
}