The asymptotic behavior of the linear transmission problem in viscoelasticity

被引：40

作者：

Alves, Margareth ^{[1
]}

Rivera, Jaime Munoz ^{[2
]}

Sepulveda, Mauricio ^{[3
,4
]}

Vera Villagran, Octavio ^{[5
]}

Zegarra Garay, Maria ^{[6
]}

机构：

[1] Univ Fed Vicosa, Vicosa, MG, Brazil

[2] LNCC, Petropolis, RJ, Brazil

[3] Univ Concepcion, CI2MA, Concepcion, Chile

[4] Univ Concepcion, DIM, Concepcion, Chile

[5] DM Univ Biobio, Concepcion, Chile

[6] U San Marcos, Fac Matemat, Lima, Peru

来源：

MATHEMATISCHE NACHRICHTEN | 2014年 / 287卷 / 5-6期

关键词：

Kelvin-Voigt; viscoelastic damping; transmission problem; semigroup; polynomial decay; Newmark-; method; 35Q74; 74-XX; SEMILINEAR WAVE-EQUATION; EXPONENTIAL DECAY; ENERGY; STABILITY; SYSTEMS;

D O I：

10.1002/mana.201200319

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：483 / 497

页数：15

共 27 条

[1]

[Anonymous], 1989, Boundary Stabilization of Thin Plates

[2] Exponential stability of a thermoelastic system with free boundary conditions without mechanical dissipation [J].