The asymptotic behavior of the linear transmission problem in viscoelasticity

Alves, M; Rivera, JM; Sepúlveda M.; Villagran, OV; Garay, MZ

Abstract

We consider a transmission problem with localized Kelvin-Voigt viscoelastic damping. Our main result is to show that the corresponding semigroup (SA(t))t0 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- method), we give some numerical examples which demonstrate this polynomial asymptotic behavior.

Más información

Título según WOS: The asymptotic behavior of the linear transmission problem in viscoelasticity
Título según SCOPUS: The asymptotic behavior of the linear transmission problem in viscoelasticity
Título de la Revista: MATHEMATISCHE NACHRICHTEN
Volumen: 287
Número: 5-6
Editorial: WILEY-V C H VERLAG GMBH
Fecha de publicación: 2014
Página de inicio: 483
Página final: 497
Idioma: English
DOI:

10.1002/mana.201200319

Notas: ISI, SCOPUS