In this paper we study the asymptotic behavior to an one-dimensional porous-elasticity problem with history. We show the lack of exponential stability when the porous dissipation or the elastic dissipation is absent. And we show the lack of analyticity and exponential stability when the porous viscosity and the elastic dissipation are present.
Pamplona, P.; Muñoz Rivera, J.E.; Quintanilla, R. On the decay of solutions for porous-elastic systems with history. "Journal of mathematical analysis and applications", 15 Juliol 2011, vol. 379, núm. 2, p. 682-705.