Exponential stability in linear thermoelasticity: the inhomogeneous case

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.

Keywords:

• Exponential stability
• energy method
• differential inequalities. (Received for Publication )

AMS:

• 35B40
• 35Q99

¹Univ. Federal do Paraá, Departamento de Matemática, 66000 Belém, Paraá, Brasil.

²National Laboratory of Scientific Computation LNCC/CNP_q, 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/CNP_q, 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/CNP_q, Rua Lauro Müller 45, Botafogo, Rio de Janeiro, 22290, RJ, Brasil and Institute of Mathematics, UFRJ, CP 68530, Rio de Janeiro, RJ, Brasil.