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Boundary value controllability and observability problems for the wave and heat equation

Published online by Cambridge University Press:  17 February 2009

K.-D. Werner
K.-D. Werner
Affiliation:
Institute of Geometry and Practical Mathematics, Technical University of Aachen, 5100 Aachen, Federal Republic of Germany
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Abstract

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In this paper, we study controllability and observability problems for the wave and heat equation in a spherical region in Rn, where the control enters in the mixed boundary condition. In the main result, we show that all “finite energy” initial states (i.e. (ω0, ν0) ∈ H1(Ω) × L2 (Ω)) can be steered to zero at time T, using a control f ∈ L2 (∂Ω × [0, T]), provided T > 2. On this basis, we use the duality principle to investigate initial observability for the wave equation. Applying the Fourier transform technique, we obtain controllability and observability results for the heat equation.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 29 , Issue 4 , April 1988, pp. 461 - 479
Copyright
Copyright © Australian Mathematical Society 1988

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