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Zeitschrift für angewandte Mathematik und Physik

, Volume 65, Issue 6, pp 1233–1249 | Cite as

Stability to 1-D thermoelastic Timoshenko beam acting on shear force

  • Dilberto da S. Almeida JúniorEmail author
  • M. L. Santos
  • J. E. Muñoz Rivera
Article

Abstract

In this paper, we study the stabilization of a new coupling to thermoelastic Timoshenko beam. In particular, we consider a thermoelastic coupling on shear force. We prove that this dissipative system is exponentially stable if and only if the velocities of waves propagations are the same, as usually occurs in Timoshenko systems with few dissipations. On the contrary, we show that the system (1.7)–(1.10) with boundary conditions (1.12) is polynomially stable, that is, that the semigroup decay as \({1/\sqrt{t}}\). Additionally, we show that this rate of decay is optimal. For the system (1.7)–(1.10) with boundary conditions (1.11), we show that the semigroup decay as \({1/\sqrt[4]{t}}\).

Mathematics Subject Classification

35B40 35B35 

Keywords

Linear thermo-elasticity Timoshenko systems Optimal decay 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Dilberto da S. Almeida Júnior
    • 1
    Email author
  • M. L. Santos
    • 1
  • J. E. Muñoz Rivera
    • 2
  1. 1.Department of MathematicsFederal University of ParáBelémBrazil
  2. 2.National Laboratory for Scientific ComputationPetrópolisBrazil

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