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Boundary coefficient control - A maximal parabolic regularity approach

Please always quote using this URN:urn:nbn:de:0296-matheon-8056
  • We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the Robin boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an Lp function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions.

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Metadaten
Author:Dietmar Hömberg, Klaus Krumbiegel, Joachim Rehberg
URN:urn:nbn:de:0296-matheon-8056
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/04/18
Release Date:2011/04/18
Tag:
Institute:Research Center Matheon
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B65 Smoothness and regularity of solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K20 Initial-boundary value problems for second-order parabolic equations
47-XX OPERATOR THEORY / 47Fxx Partial differential operators [See also 35Pxx, 58Jxx] / 47F05 Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J20 Optimal control problems involving partial differential equations
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K20 Problems involving partial differential equations
Preprint Number:775
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