A transmission problem for the Timoshenko system

Abstract

Abstract. In this work we study a transmission problem for the model of beams developed by S.P. Timoshenko [10]. We consider the case of mixed material, that is, a part of the beam has friction and the other is purely elastic. We show that for this type of material, the dissipation produced by the frictional part is strong enough to produce exponential decay of the solution, no matter how small is its size. We use the method of energy to prove exponential decay for the solution.Mathematical subject classification: 35J55, 35J77, 93C20.

Decay Property for the Timoshenko System With Fourier's Type Heat Conduction

“…We refer to [12,13,16] for frictional dissipation case, [5,14,15] for thermal dissipation case, and [1,2,8,9] for memory-type dissipation case.…”

Viscoelastic Timoshenko Beams with Occasionally Constant Relaxation Functions

“…The right hand side inequality in (19) implies that E(t) ≤ C 4 /γ (t), t ≥ t 0 for some positive constant C 4 . The continuity of E(t) and boundedness of the interval [0, t 0 ] allows us to conclude.…”

“…Linear and nonlinear internal frictional dampings have been considered in the papers of Soufyane [24,25], Shi and Feng [21], Soufyane and Wehbe [26], Xu and Yung [32,33], Muñoz Rivera and Racke [15], Raposo et al [18,19] and Alabau-Boussouira [1]. The problems were of the form ρ 1 ϕ tt − k(ϕ x + ψ) x + f (ϕ t ) = 0, 0 < x < l,…”

Semigrupos Aplicados a Sistemas Dissipativos em EDP

“…Assumiremos a existência e unicidade de solução forte para o problema (3.2.5)-(3.2.7), a qual pode ser provada utilizando semigrupos ( ver A. Soufyane [14] ) ou método de Faedo-Galerkin ( ver C. A. Raposo [11] ). O problema é bem posto para dados iniciais…”