Abstract
The time dependent system of linear thermoelasticity for isotropic bodies but totally inhomogeneous is considered. Recent results (in the homogeneous case) due to D. Henry et al. [2] and J. Rivera [7, 8] show that uniform rates of decay of the total energy are valid only in one dimension for such systems. We show that in case of isotropic inhomogeneous bodies there are special situations where we can stabilize (exponentially) the system for arbitrary dimensions. We apply the above result to study the convergence of the solution to the steady state in a exponential fashion. Our result extends recent work on the subject [6]. Our proofs are elementary.
1Univ. Federal do Paraá, Departamento de Matemática, 66000 Belém, Paraá, Brasil.
2National Laboratory of Scientific Computation LNCC/CNPq, Rua Lauro Müller 45, Botafogo, Rio de Janeiro, 22290, RJ, Brasil and Institute of Mathematics, UFRJ, CP 68530, Rio de Janeiro, RJ, Brasil.
1Univ. Federal do Paraá, Departamento de Matemática, 66000 Belém, Paraá, Brasil.
2National Laboratory of Scientific Computation LNCC/CNPq, Rua Lauro Müller 45, Botafogo, Rio de Janeiro, 22290, RJ, Brasil and Institute of Mathematics, UFRJ, CP 68530, Rio de Janeiro, RJ, Brasil.
Notes
1Univ. Federal do Paraá, Departamento de Matemática, 66000 Belém, Paraá, Brasil.
2National Laboratory of Scientific Computation LNCC/CNPq, Rua Lauro Müller 45, Botafogo, Rio de Janeiro, 22290, RJ, Brasil and Institute of Mathematics, UFRJ, CP 68530, Rio de Janeiro, RJ, Brasil.