Porous elastic system with Kelvin–Voigt: analyticity and optimal decay rate

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.

COMMUNICATED BY:

• M. Fang

Keywords:

• Porous-elasticity
• lack of stability
• analytic semigroup
• polynomial decay
• optimality

2010 Mathematics Subject Classifications:

• 35B35 Stability
• 35B40 Asymptotic behavior ofsolutions

Disclosure statement

No potential conflict of interest was reported by the author(s).