Abstract
We prove that the linear system of thermoelasticity with various boundary conditions is controllable in the following sense: If the control time is large enough and we act in the equations of displacement by means of a control supported in a neighborhood of the boundary of the thermoelastic body, then we may control exactly the displacement and simultaneously the temperature in an approximate way. We consider the following two cases: a) The displacement satisfies Dirichlet boundary conditions and the temperature takes Neumann zero boundary value; b) The displacement satisfies Neumann boundary conditions and the temperature vanishes at the boundary. The method of proof is inspired in our earlier work where the same result was proved for the case where both displacement and temperature satisfy Dirichlet boundary conditions.
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References
C. Fabre, J. P. Puel and E. Zuazua, Contrôlabilité approchée de l équation de la chaleur semilinéaire, C. R. Acad. Sci. Paris, 315, série I, 1992, 807–812.
C. Fabre, J. P. Puel and E. Zuazua, Approximate controllability of the semilinear heat equation, Proc. Royal Soc. Edinburgh, to appear.
C. Fabre, J. P. Puel and E. Zuazua, Contrôlabilité approché de léquation de la chaleur linéaire avec des contrôles de norme L∞ minimale, C. R. Acad. Sci. Paris, 316, série I, 1993, 679–684.
C. Fabre, J. P. Puel and E. Zuazua, On the density of the range of the semigroup for semilinear heat equations, IMA Preprint Series, # 1093, 1992.
S. W. Hansen, Boundary control of a one-dimensional, linear, thermoelastic rod, SIAM J. Cont. Optim., to appear.
D. Henry, O. Lopes and A. Perissinitto, On the essential spectrum of a semigroup of thermoelasticity, preprint.
F. John, Partial Differential Equations ,Applied Mathematical Sciences 1, 4th edition, Springer Verlag, New York, 1986.
J. E. Lagnese, The reachability problem for thermoelastic plates, Arch. Rat. Mech. Anal., 112 (1990), 223–267.
J. E. Lagnese and J. L. Lions, Modelling, Analysis and Control of Thin Plates ,Masson, RMA 6, Paris, 1988.
J. L. Lions, Remarks on approximate controllability, J. Analyse. Math., 59, 1992, 103– 116.
K. Narukawa, Boundary value control of thermoelastic systems, Hiroshima Math. J., 13 (1983), 227–272.
E. Zuazua, Contrôlabilité du Systeme de la thermoélasticité, C. R. Acad. Sci. Paris, 317 (1993), 371–376.
E. Zuazua, Contrôlabilité du système de la thermoélasticité sans restrictions sur les paramètres de couplage, C. R. Acad. Sci. Paris, 318 (1994), 643–648.
E. Zuazua, Controllability of the linear system of thermoelasticity, preprint. Enrique Zuazua Departamento de Matemática Aplicada Universidad Complutense 28040 Madrid, Spain
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Zuazua, E. (1994). Controllability of the Linear System of Thermoelasticity: Dirichlet-Neumann Boundary Conditions. In: Desch, W., Kappel, F., Kunisch, K. (eds) Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena. ISNM International Series of Numerical Mathematics, vol 118. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8530-0_22
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DOI: https://doi.org/10.1007/978-3-0348-8530-0_22
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9666-5
Online ISBN: 978-3-0348-8530-0
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