Geodesic
Parabolic optimal control problems on evolving surfaces subject to point-wise box constraints on the control – theory and numerical realization
Morten Vierling1
1Universität Hamburg, Germany
Interfaces and free boundaries, Tome 16 (2014) no. 2, pp. 137-173

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DOI

We consider control-constrained linear-quadratic optimal control problems on evolving hypersurfaces in Rn+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.
DOI : 10.4171/ifb/316
Classification : 58-XX, 35-XX, 49-XX
Mots-clés : Evolving surfaces, weak solutions, parabolic optimal control, error estimates

Morten Vierling  1

1 Universität Hamburg, Germany 
Morten Vierling. Parabolic optimal control problems on evolving surfaces subject to point-wise box constraints on the control – theory and numerical realization. Interfaces and free boundaries, Tome 16 (2014) no. 2, pp. 137-173. doi: 10.4171/ifb/316
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     title = {Parabolic optimal control problems on evolving surfaces subject to point-wise box constraints on the control {\textendash} theory and numerical realization},
     journal = {Interfaces and free boundaries},
     pages = {137--173},
     year = {2014},
     volume = {16},
     number = {2},
     doi = {10.4171/ifb/316},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/316/}
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