Aissa GUESMIA , Salim MESSAOUDI . SOME STABILITY RESULTS FOR TIMOSHENKO SYSTEMS WITH COOPERATIVE FRICTIONAL AND INFINITE-MEMORY DAMPINGS IN THE DISPLACEMENT[J]. Acta mathematica scientia, Series B, 2016 , 36(1) : 1 -33 . DOI: 10.1016/S0252-9602(15)30075-8

[1] Alabau-Boussouira F. Asymptotic behavior for Timoshenko beams subject to a single nonlinear feedback control. Nonlinear Diff Equa Appl, 2007, 14:643-669
[2] Almeida Júnior D S, Santos M L, Muñoz Rivera J E. Stability to weakly dissipative Timoshenko systems. Math Meth Appl Sci, 2013, 36:1965-1976
[3] Almeida Júnior D S, Santos M L, Muñoz Rivera J E. Stability to 1-D thermoelastic Timoshenko beam acting on shear force. Z Angew Math Phys, 2014, 65(6):1233-1249
[4] Ammar-Khodja F, Benabdallah A, Muñoz Rivera J E, Racke R. Energy decay for Timoshenko systems of memory type. J Diff Equa, 2003, 194:82-115
[5] Cavalcanti M M, Oquendo H P. Frictional versus viscoelastic damping in a semilinear wave equation. SIAM J Control and Optim, 2003, 42:1310-1324
[6] Dafermos C M. Asymptotic stability in viscoelasticity. Arch Rational Mech Anal, 1970, 37:297-308
[7] Fernández Sare H D, Muñoz Rivera J E. Stability of Timoshenko systems with past history. J Math Anal Appl, 2008, 339:482-502
[8] Fernández Sare H D, Racke R. On the stability of damped Timoshenko systems:Cattaneo versus Fourier's law. Arch Rational Mech Anal, 2009, 194:221-251
[9] Guesmia A. Asymptotic stability of abstract dissipative systems with infinite memory. J Math Anal Appl, 2011, 382:748-760
[10] Guesmia A. On the stabilization for Timoshenko system with past history and frictional damping controls. Palestine J Math, 2013, 2:187-214
[11] Guesmia A. Asymptotic behavior for coupled abstract evolution equations with one infinite memory. Appl Anal, 2015, 94(1):184-217
[12] Guesmia A, Messaoudi S A. On the control of solutions of a viscoelastic equation. Appl Math Comput, 2008, 206:589-597
[13] Guesmia A, Messaoudi S A. General energy decay estimates of Timoshenko systems with frictional versus viscoelastic damping. Math Meth Appl Sci, 2009, 32:2102-2122
[14] Guesmia A, Messaoudi S A, Soufyane A. Stabilization of a linear Timoshenko system with infinite history and applications to the Timoshenko-Heat systems. Elec J Diff Equa, 2012, 2012:1-45
[15] Guesmia A, Messaoudi S, Wehbe A. Uniform decay in mildly damped Timoshenko systems with non-equal wave speed propagation. Dyn Syst Appl, 2012, 21:133-146
[16] Guesmia A, Messaoudi S A. On the stabilization of Timoshenko systems with memory and different speeds of wave propagation. Appl Math Comput, 2013, 219:9424-9437
[17] Guesmia A, Messaoudi S A. A general stability result in a Timoshenko system with infinite memory:A new approach. Math Meth Appl Sci, 2014, 37:384-392
[18] Kim J U, Renardy Y. Boundary control of the Timoshenko beam. SIAM J Control Opt, 1987, 25:1417-1429
[19] Komornik V. Exact Controllability and Stabilization. The Multiplier Method. Paris:Masson-John Wiley, 1994
[20] Lasiecka I, Tataru D. Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping, Differ Integral Equ, 1993, 6:507-533
[21] Lasiecka I, Toundykov D. Regularity of higher energies of wave equation with nonlinear localized damping and source terms. Nonl Anal:TMA, 2008, 69:898-910
[22] Liu W J, Zuazua E. Decay rates for dissipative wave equations. Ricerche di Matematica, 1999, 48:61-75
[23] Messaoudi S A, Mustafa M I. On the internal and boundary stabilization of Timoshenko beams. Nonlinear Diff Equa Appl, 2008, 15:655-671
[24] Messaoudi S A, Mustafa M I. On the stabilization of the Timoshenko system by a weak nonlinear dissipation. Math Meth Appl Sci, 2009, 32:454-469
[25] Messaoudi S A, Mustafa M I. A stability result in a memory-type Timoshenko system. Dyn Syst Appl, 2009, 18:457-468
[26] Messaoudi S A, Michael P, Said-Houari B. Nonlinear Damped Timoshenko systems with second:Global existence and exponential stability. Math Meth Appl Sci, 2009, 32:505-534
[27] Messaoudi S A, Said-Houari Belkacem. Uniform decay in a Timoshenko-type system with past history. J Math Anal Appl, 2009, 360:459-475
[28] Muñoz Rivera J E, Racke R. Mildly dissipative nonlinear Timoshenko systems-global existence and exponential stability. J Math Anal Appl, 2002, 276:248-278
[29] Muñoz Rivera J E, Racke R. Global stability for damped Timoshenko systems. Disc Contin Dyn Syst, 2003, 9:1625-1639
[30] Muñoz Rivera J E, Racke R. Timoshenko systems with indefinite damping. J Math Anal Appl, 2008, 341:1068-1083
[31] Mustafa M I, Messaoudi S A. General energy decay rates for a weakly damped Timoshenko system. Dyn Control Sys, 2010, 16:211-226
[32] Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. New York:Springer-Verlag, 1983
[33] Racke R, Said-Houari B. Global existence and decay property of the Timoshenko system in thermoelasticity with second sound. Nonl Anal, 2012, 75:4957-4973
[34] Raposo C A, Ferreira J, Santos M L, Castro N N O. Exponential stability for the Timoshenko system with two week dampings. Appl Math Lett, 2005, 18:535-541
[35] Said-Houari B, Kasimov A. Decay property of Timoshenko system in thermoelasticity. Math Meth Appl Sci, 2012, 35:314-333
[36] Said-Houari B, Kasimov A. Damping by heat conduction in the Timoshenko system:Fourier and Cattaneo are the same. J Diff Equ, 2013, 255:611-632
[37] Santos M L, Almeida Júnior D S, Muñoz Rivera J E. The stability number of the Timoshenko system with second sound. J Diff Equ, 2012, 253:2715-2733
[38] Soufyane A, Wehbe A. Uniform stabilization for the Timoshenko beam by a locally distributed damping. Elec J Diff Equ, 2003, 29:1-14
[39] Timoshenko S. On the correction for shear of the differential equation for transverse vibrations of prismaticbars. Philisophical Magazine, 1921, 41:744-746