Exponential stability of the semigroup associated with a thermoelastic system

Abstract

Abstract. In this paper it is proved that the semigroup associated with the onedimensional thermoelastic system with Dirichlet boundary conditions is an exponen-12 2 tially stable C0-semigroup of contraction on the space H0 x L x L . The technique of the proof is completely different from the usual energy method. It is shown that the exponential decay in 3 (s/) recently obtained by Revira is a consequence of our main result. An important application of our main result to the Linear-QuadraticGaussian optimal control problem is also discussed.

Stability of Abstract Linear Thermoelastic Systems With Memory

“…In this direction, we quote some works dealing with thermoelasic rods and plates. 1,10,11,[15][16][17][19][20][21]23,25 The plan of the paper is as follows. In Sec.…”

Uniform stabilization of the higher-dimensional system of thermoelasticity with a nonlinear boundary feedback

“…Note that condition (1.2) is weaker than the following usual condition on the Lame coefficients (see [44] and [13, p. 414]) nX + 2fx > 0. (1)(2)(3) Extensive work has been done on the problem of stabilization for system (1.1) (see [5,9,7,12,17,20,27,33,37,40,42,43,45,46,47,48]). We give here a brief description of the existing literature.…”

“…Furthermore, in the case of one space dimension, it has been shown (see [9,17,20,40]) that the energy E(u, 6, t) of system (1.1) associated with various boundary conditions decays to zero exponentially.…”

Stability of coupled systems

“…The interest here is that, in the one-dimensional case (the one-dimensional thermoelasticity system), the exponential stability remains even if a ≡ 0 (see [8]). …”