Controllability of the Linear System of Thermoelasticity: Dirichlet-Neumann Boundary Conditions
Enrique Zuazua · Birkhäuser Basel eBooks · 1994
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.