General decay for a viscoelastic-type Timoshenko system with thermoelasticity of type III

Abstract

We consider a one-dimensional thermoelastic Timoshenko system, where the heat conduction is given by Green and Naghdi theories and acting on shear force. We prove that the unique damping given by the memory is sufficiently strong to stabilize the system exponentially, depending on a new relationship between the coefficients of the system and under some assumptions on the kernel of the memory term. In fact, we establish a general decay result, of which exponential and polynomial decay results are special cases.

Keywords:

• Timoshenko system
• thermoelasticity of type III
• general decay
• Lyapunov functional

2010 Mathematics Subject Classifications::

• 35B35
• 74F05
• 93D20
• 74D05

Acknowledgments

The authors wish to thank deeply the editors and referees for their useful remarks and their careful reading of the proofs presented in this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).