General decay result for thermoelastic beam equation system with time-varying delay

Abstract In this paper, we study a thermoelastic beam system with internal time-varying delay. We show that the damping and viscoelastic terms are strong enough to stabilize the system at a general decay rate under suitable assumptions on the time-varying delay and the relaxation function.

[1]  Jorge Ferreira,et al.  Existence, uniqueness and uniform decay for the nonlinear beam degenerate equation with weak damping , 2004, Appl. Math. Comput..

[2]  Serge Nicaise,et al.  Stability and Instability Results of the Wave Equation with a Delay Term in the Boundary or Internal Feedbacks , 2006, SIAM J. Control. Optim..

[3]  M. I. Mustafa Asymptotic behavior of second sound thermoelasticity with internal time-varying delay , 2013 .

[4]  Song Jiang,et al.  Asymptotic stability and global existence in thermoelasticity with symmetry , 1998 .

[5]  Enrique Zuazua,et al.  Exponential Decay for The Semilinear Wave Equation with Locally Distributed Damping , 1990 .

[6]  H. Koch Slow decay in linear thermoelasticity , 2000 .

[7]  Enrique Zuazua,et al.  Decay Rates for the Three‐Dimensional Linear System of Thermoelasticity , 1999 .

[8]  S. Messaoudi,et al.  Energy decay result in a Timoshenko-type system of thermoelasticity of type III with distributive delay , 2013 .

[9]  R. Racke Thermoelasticity with second sound—exponential stability in linear and non‐linear 1‐d , 2002 .

[10]  Sun Hye Park,et al.  Decay rate estimates for a weak viscoelastic beam equation with time-varying delay , 2014, Appl. Math. Lett..

[11]  Irena Lasiecka,et al.  Existence and Exponential Decay of Solutions to a Quasilinear Thermoelastic Plate System , 2008 .

[12]  Yamina Laskri,et al.  A stability result of a Timoshenko system with a delay term in the internal feedback , 2010, Appl. Math. Comput..

[13]  Mokhtar Kirane,et al.  Stability result for the Timoshenko system with a time-varying delayterm in the internal feedbacks , 2010 .

[14]  Reinhard Racke,et al.  Instability of coupled systems with delay , 2012 .

[15]  S. Messaoudi General Decay of Solutions of a Weak Viscoelastic Equation , 2011 .

[16]  Kangsheng Liu Locally Distributed Control and Damping for the Conservative Systems , 1997 .