Exact controllability of a thermoelastic system with control in the thermal component only

In this work we give a result of exact controllability for a thermoelastic system in which the control term is placed solely in the thermal equation. With such an indirect control input, one is able to control exactly the displacement of the plate, as well as the temperature. This exact controllability occurs in arbitrarily small time. In the case that the moment of inertia parameter for the plate is absent (i.e., = 0 below), then one is provided here with a result of exact controllability for a thermoelastic system which is modelled by the generator of an analytic semigroup. The proof here depends upon a multiplier method so as to attain the associated observability inequality. The particular multiplier invoked is of an operator theoretic nature, and has been used previously by the author in deriving stability results for this pde model. Department of Mathematics, Texas Tech University, Lubbock, Texas 79409{1042, USA. Research supported in part by the NSF Grant DMS-9710981.

[1]  J. Lagnese.  Boundary Stabilization of Thin Plates , 1987 .

[2]  R. Triggiani,et al.  Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions , 1992 .

[3]  John E. Lagnese,et al.  The reachability problem for thermoelastic plates , 1990 .

[4]  Jerzy Zabczyk,et al.  Mathematical control theory - an introduction , 1992, Systems & Control: Foundations & Applications.

[5]  R. Triggiani.  Constructive steering control functions for linear systems and abstract rank conditions , 1992 .

[6]  Scott W. Hansen,et al.  Boundary Control of a Linear Thermoelastic Beam , 1997 .

[7]  Enrique Zuazua,et al.  Controllability of the linear system of thermoelastic plates , 1996, Advances in Differential Equations.

[8]  Uniform Decays in Nonlinear Thermoelastic Systems , 1998 .

[9]  George Avalos,et al.  THE EXPONENTIAL STABILITY OF A COUPLED HYPERBOLIC/PARABOLIC SYSTEM ARISING IN STRUCTURAL ACOUSTICS , 1996 .

[10]  Irena Lasiecka,et al.  Exponential stability of a thermoelastic system without mechanical dissipation , 1995 .

[11]  Zhuangyi Liu,et al.  A note on the equations of a thermoelastic plate , 1995 .

[12]  V. Komornik.  Exact Controllability and Stabilization: The Multiplier Method , 1995 .

[13]  D. Russell.  Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions , 1978 .

[14]  P. Grisvard,et al.  Caractérisation de quelques espaces d'interpolation , 1967 .

[15]  J. Lions,et al.  Non-homogeneous boundary value problems and applications , 1972 .

[16]  Irena Lasiecka,et al.  Exact controllability and uniform stabilization of Kirchoff plates with boundary control only on Δw¦Σ and homogeneous boundary displacement , 1991 .