Optimal distributed control of the wave equation subject to state constraints

Gugat M, Keimer A, Leugering G (2009)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2009

Journal

ZAMM - Zeitschrift für angewandte Mathematik und Mechanik Wiley-VCH Verlag

Publisher: Wiley-VCH Verlag

Book Volume: 89

Pages Range: 420-444

Journal Issue: 6

URI: http://www3.interscience.wiley.com/journal/5007542/home

DOI: 10.1002/zamm.200800196

Abstract

The Lavrentiev regularization method is a tool to improve the regularity of the Lagrange multipliers in pde constrained optimal control problems with state constraints. It has already been used for problems with parabolic and elliptic systems. In this paper we consider Lavrentiev regularization for problems with a hyperbolic system, namely the scalar wave equation. We show that also in this case the regularization yields multipliers in the Hilbert space L². We present numerical exam-ples, where we compare the Lavrentiev regularization, Lavrentiev Prox regularization, a fixed point iteration to improve feasibility, and a penalty method. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Authors with CRIS profile

Martin Gugat Lehrstuhl für Angewandte Mathematik Alexander Keimer
Günter Leugering Lehrstuhl für Angewandte Mathematik

How to cite

APA:

Gugat, M., Keimer, A., & Leugering, G. (2009). Optimal distributed control of the wave equation subject to state constraints. ZAMM - Zeitschrift für angewandte Mathematik und Mechanik, 89(6), 420-444. https://doi.org/10.1002/zamm.200800196

MLA:

Gugat, Martin, Alexander Keimer, and Günter Leugering. "Optimal distributed control of the wave equation subject to state constraints." ZAMM - Zeitschrift für angewandte Mathematik und Mechanik 89.6 (2009): 420-444.

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