Decay property of regularity-loss type of solutions in elastic solids with voids

Abstract

In this article, we consider two porous systems of nonclassical thermoelasticity in the whole real line. We discuss the long-time behaviour of the solutions in the presence of a strong damping acting, together with the heat effect, on the elastic equation and establish several decay results. Those decay results are shown to be very slow and of regularity-loss type. Some improvements of the decay rates have also been given, provided that the initial data belong to some weighted spaces.

Keywords:

• decay rate
• heat conduction
• thermoelasticity

AMS Subject Classifications::

• 35B37
• 35L55
• 74D05
• 93D15
• 93D20

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Erratum

Acknowledgements

This work was finalized during a short visit of the first author to KFUPM. This author thanks KFUPM for its kind hospitality. Both the authors thank KFUPM and KAUST for their support. This work has been partially funded by KFUPM under Project # SB 101008.