Optimal Decay Rate for Unidimensional Thermoelastic Problem within the Green-Lindsay Model

Abstract

In this article we consider the system of generalized thermoelasticity under Green–Lindsay model in one dimension with Dirichlet–Neumann boundary conditions. First, the roots of the characteristic polynomial are investigated by applying an approach based on the implicit function theorem. Then we prove the exponential decay of the associated energy and describe the optimal decay rate. The numerical calculation of the corresponding characteristic roots is done for different real materials. Then another approach based on Hurwitz criterion is applied to obtain the decay rate analytically. Finally, we present a discussion of the decay rate given by both approaches, as well as a comparison with already-existing results for Lord–Shulman and classical models of thermoelasticity.

Keywords:

• Green–Lindsay
• Hurwitz criterion
• Implicit function theorem
• Optimal decay rate

ACKNOWLEDGMENTS

The authors would like to thank the reviewer for her/his critical review and valuable comments which thoroughly improved the paper.