TY - MGZN
AU - MagaĆ±a, A.
AU - Quintanilla, R.
T2 - Mathematical methods in the applied sciences
Y1 - 2020
VL - 43
IS - 11
SP - 6921
EP - 6937
DO - 10.1002/mma.6438
UR - https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.6438
AB - In this paper we consider the theory of thermoelasticity with a double porosity structure in the context of the Green-Naghdi types II and III heat conduction models. For the type II, the problem is given by four hyperbolic equations and it is conservative (there is no energy dissipation). We introduce in the system a couple of dissipation mechanisms in order to obtain the exponential de- cay of the solutions. To be precise, we introduce a pair of the following damping mechanisms: viscoelasticity, viscoporosities and thermal dissipation. We prove that the system is exponentially stable in three different scenarios: viscoporosity in one structure jointly with thermal dissipation, viscoporosity in each structure, and viscoporosity in one structure jointly with viscoelasticity. However, if viscoelasticity and thermal dissipation are considered together, undamped solutions can be obtained.
TI - Exponential decay in one-dimensional Type II/III thermoelasticity with two porosities
ER -