Exponential stability of serially connected thermoelastic system of type II with nodal damping

Abstract

In this paper, we consider a serially connected thermoelastic rods of type II, where the heat conduction is described by the theories of Green and Naghdi. Using the frequency domain method, together with multiplier techniques, we show that the energy of this multi-connected system decays to zero exponentially in the presence of boundary and joint damping, by estimating the uniform boundedness of the norm of the resolvent operator along the imaginary axis.

Keywords:

• thermoelasticity
• joint damping
• spectrum
• stability

AMS Subject Classifications:

• 74F05
• 35B40
• 35Q70

Acknowledgments

The authors would like to thank the referees for their useful and helpful comments and suggestions.