Spatial and temporal behavior in the theory of thermoelasticity for solids with double porosity

ABSTRACT

In this article, we study the spatial and the temporal behavior of solutions to the initial boundary value problem associated with the linear theory of thermoelastic materials with a double porosity structure. We consider two appropriate time-weighted integral measures and we deduce some exponential estimates that describe the spatial behavior of solutions. For bounded bodies, we obtain estimates of Saint-Venant type, while for unbounded bodies we deduce some alternatives of Phragmén–Lindelöf type. The temporal behavior of solutions is described using the Cesáro means of various parts of the total energy.

KEYWORDS:

• Asymptotic behavior
• spatial behavior
• spatial decay and growth
• thermoelasticity with double porosity structure