TY - JOUR
T1 - The asymptotic behavior of the linear transmission problem in viscoelasticity
AU - Alves, Margareth
AU - Rivera, Jaime Muñoz
AU - Sepúlveda, Mauricio
AU - Villagrán, Octavio Vera
AU - Garay, María Zegarra
PY - 2014/1/1
Y1 - 2014/1/1
N2 - 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.
AB - 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.
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U2 - 10.1002/mana.201200319
DO - 10.1002/mana.201200319
M3 - Article
SN - 0025-584X
SP - 483
EP - 497
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
ER -