In this paper, we consider a linear thermoelastic Timoshenko system with memory effects where the thermoelastic coupling is acting on shear force under Neumann–Dirichlet–Dirichlet boundary conditions. The same system with fully Dirichlet boundary conditions was considered by Messaoudi and Fareh (Nonlinear Anal TMA 74(18):6895–6906, 2011, Acta Math Sci 33(1):23–40, 2013), but they obtained a general stability result which depends on the speeds of wave propagation. In our case, we obtained a general stability result irrespective of the wave speeds of the system.
Timoshenko Linear thermoelasticity General decay Relaxation function
This is a preview of subscription content, log in to check access.
Guesmia, A., Messaoudi, S.A.: On the control of a viscoelastic damped Timoshenko-type system. Appl. Math. Comput. 2062, 589–597 (2008)MathSciNetMATHGoogle Scholar
Guesmia, A., Messaoudi, S.A.: General energy decay estimates of Timoshenko systems with frictional versus viscoelastic damping. Math. Meth. Appl. Sci. 32(16), 2102–2122 (2009)MathSciNetCrossRefMATHGoogle Scholar
Guesmia, A., Messaoudi, S.A., Soufyane, A.: Stabilization of a linear Timoshenko system with infinite history and applications to the Timoshenko-heat systems. Electron. J. Differ. Equ. 2012(193), 1–45 (2012)MathSciNetMATHGoogle Scholar
Han, S.M., Benaroya, H., Wei, T.: Dynamics of transversely vibrating beams using four engineering theories. J. Sound Vib. 225(5), 935–988 (1999)ADSCrossRefMATHGoogle Scholar
Messaoudi, S.A., Fareh, A.: General decay for a porous thermoelastic system with memory: the case of equal speeds. Nonlinear Anal. TMA 74(18), 6895–6906 (2011)MathSciNetCrossRefMATHGoogle Scholar
Messaoudi, S.A., Fareh, A.: General decay for a porous thermoelastic system with memory: the case of nonequal speeds. Acta Math. Sci. 33(1), 23–40 (2013)MathSciNetCrossRefMATHGoogle Scholar
Messaoudi, S.A., Pokojovy, M., SaidHouari, B.: Nonlinear damped Timoshenko systems with second soundglobal existence and exponential stability. Math. Meth. Appl. Sci. 32(5), 505–534 (2009)CrossRefMATHGoogle Scholar
Muñoz Rivera, J.E., Racke, R.: Mildly dissipative nonlinear Timoshenko systems-global existence and exponential stability. J. Math. Anal. Appl. 276(1), 248–278 (2002)MathSciNetCrossRefMATHGoogle Scholar
Raposo, C.A., Ferreira, J., Santos, M.L., Castro, N.N.O.: Exponential stability for the Timoshenko system with two weak dampings. Appl. Math. Lett. 18(5), 535–541 (2005)MathSciNetCrossRefMATHGoogle Scholar
Soufyane, A., Whebe, A.: Uniform stabilization for the Timoshenko beam by a locally distributed damping. Electron. J. Differ. Equ. 2003(29), 1–14 (2003)MathSciNetMATHGoogle Scholar