Optimal control of the thermistor problem in three spatial dimensions, part 1: Existence of optimal solutions

Meinlschmidt H, Meyer C, Rehberg J (2017)

Publication Type: Journal article

Publication year: 2017

Journal

SIAM Journal on Control and Optimization Society for Industrial and Applied Mathematics

Book Volume: 55

Pages Range: 2876-2904

Journal Issue: 5

DOI: 10.1137/16M1072644

Abstract

This paper is concerned with the state-constrained optimal control of the threedimensional thermistor problem, a fully quasi-linear coupled system of a parabolic and elliptic PDEs with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Local existence, uniqueness, and continuity for the state system are derived by employing maximal parabolic regularity in the fundamental theorem of Prüss. Global solutions and controls admitting such are addressed and existence of optimal controls is shown if the temperature gradient is under control. This work is the first of two papers on the three-dimensional thermistor problem.

Authors with CRIS profile

Hannes Meinlschmidt

Involved external institutions

Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) - Leibniz-Institut im Forschungsverbund Berlin e. V. DE Germany (DE) Technische Universität Dortmund DE Germany (DE) Technische Universität Darmstadt DE Germany (DE)

How to cite

APA:

Meinlschmidt, H., Meyer, C., & Rehberg, J. (2017). Optimal control of the thermistor problem in three spatial dimensions, part 1: Existence of optimal solutions. SIAM Journal on Control and Optimization, 55(5), 2876-2904. https://dx.doi.org/10.1137/16M1072644

MLA:

Meinlschmidt, Hannes, Christian Meyer, and J. Rehberg. "Optimal control of the thermistor problem in three spatial dimensions, part 1: Existence of optimal solutions." SIAM Journal on Control and Optimization 55.5 (2017): 2876-2904.

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