Porous elastic system with Kelvin–Voigt: analyticity and optimal decay rate. Issue 8 (24th May 2022) - Oliveira, M. L. S.; Maciel, E. S.; Dos Santos, M. J.
ABSTRACT: In this work we analyze the porous elastic system with a viscoelastic dissipative mechanism of Kelvin–Voigt type. We prove that the semigroup associated with the model is analytic if and only if the viscoelastic damping is present in both equations of the system. Otherwise, there exist lack of exponential stability, independently of any relationship between the coefficients. This result is different to all others related to porous-elastic model with partial dissipation. In this case we prove that the semigroup decays as t − 1 / 2 . Moreover we show that the rate is optimal.