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Main Title: Optimal Control of a Semilinear PDE with Nonlocal Radiation Interface Conditions
Author(s): Meyer, Christian
Philip, Peter
Tröltzsch, Fredi
Type: Research Paper
Abstract: We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffuse-gray conductive-radiative heat transfer. The problem arises from the aim to optimize the temperature gradient within crystal growth by the physical vapor transport (PVT) method. Based on a minimum principle for the semilinear equation as well as $L^\infty$-estimates for the weak solution, we establish the existence of an optimal solution as well as necessary optimality conditions. The theoretical results are illustrated by results of numerical computations.
Subject(s): optimal control
semilinear elliptic equations
nonlocal interface conditions
boundedness of solutions
Issue Date: 22-Oct-2004
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 49K20 Problems involving partial differential equations
35J65 Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE
49J20 Optimal control problems involving partial differential equations
80M50 Optimization
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2004, 33
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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