Energy decay of the Bresse system by two thermo-viscoelastic dampings

  • Selma Boulechfar
  • Salah Zitouni Partial of defferential equation, departement of mathematics Souk Ahras University
  • Abdelhak Djebabla Laboratory of Applied Mathematics, University Badji Mokhtar,\\ Department of Mathematics, B. P. 12 Annaba 23141, Algeria
  • Amar Guesmia Department of Mathematics, Faculty of Sciences, University 20 Ao^ut 1955 of Skikda, P.O. Box 26, Skikda 21000, Algeria


In this paper, we consider a one-dimensional linear Bresse system without using any internal or boundary damping, where this system produces a dissipation of energy only when complemented by two thermo-viscoelastic damping, knowing that the type of thermal diffusion used was introduced by Green and Naghdi. We establish the stability of the system with Drichlet boundary conditions and for the case of equal speeds of wave propagation, this is done by selecting suitable Lyapunov functionals.