We consider a transmission problem with localized Kelvin-Voigt viscoelastic damping. Our main result is to show that the corresponding semigroup (SA(t))t≥0 is not exponentially stable, but the solution of the system decays polynomially to zero as 1/t2 when the initial data are taken over the domain D(A). Moreover, we prove that this rate of decay is optimal. Finally, using a second order scheme that ensures the decay of energy (Newmark-β method), we give some numerical examples which demonstrate this polynomial asymptotic behavior. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Alves, M., Rivera, J. M., Sepúlveda, M., Villagrán, O. V., & Garay, M. Z. (2014). The asymptotic behavior of the linear transmission problem in viscoelasticity. Mathematische Nachrichten, 483-497. https://doi.org/10.1002/mana.201200319