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Boundary value control problems involving the bessel differential operator

Published online by Cambridge University Press:  17 February 2009

K.-D. Werner
K.-D. Werner
Affiliation:
This paper was written during the author's stay at the School of Mathematics, University of New South Wales, N.S.W., 2033, Australia. (Present address: Institute of Geometry and Practical Mathematics, Technical University of Aachen, Templergraben 55, 5100 Aachen, Fed. Rep. of Germany)
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Abstract

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In this paper, we consider the hyperbolic partial differential equation wrr = wrr + 1/r wr − ν2 /r2w, where v ≥ 1/2 or ν = 0 is aprameter, with the Dirichlet, Neumann and mixed boundary conditions. The boundary controllability for such problems is investigated. The main resutl is that all “finite energy” intial states can be steered to the zero state in time T, using a control f ∈ L2 (0, T), provided T > 2. Furthermore, necessary conditions for controllability are also presented.

Type
Research Article
Information
The ANZIAM Journal , Volume 27 , Issue 4 , April 1986 , pp. 453 - 472
Copyright
Copyright © Australian Mathematical Society 1986

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