Control-constrained parabolic optimal control problems on evolving\n surfaces - theory and variational discretization

2011/06/03 by Morten Vierling, Vierling, Morten
Computer Science · Engineering · Mathematics · #35D30 #35R01 #49J20 #49Q99 #58J35 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Electrical engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1106.0622

openalex publication_date 2011/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider control-constrained linear-quadratic optimal control problems on\nevolving surfaces. In order to formulate well-posed problems, we prove\nexistence and uniqueness of weak solutions for the state equation, in the sense\nof vector-valued distributions. We then carry out and prove convergence of the\nvariational discretization of a distributed optimal control problem. In the\nprocess, we investigate the convergence of a fully discrete approximation of\nthe state equation, and obtain optimal orders of convergence under weak\nregularity assumptions. We conclude with a numerical example.\n

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