ON A KELVIN-VOIGT VISCOELASTIC WAVE EQUATION WITH STRONG DELAY

被引：6

作者：

Demchenko, Hanna ^{[1
]}

Anikushyn, Andrii ^{[2
]}

Pokojovy, Michael ^{[3
]}

机构：

[1] Masaryk Univ, Fac Econ & Adm, Brno 60200, Czech Republic

[2] Taras Shevcheno Natl Univ Kyiv, Dept Comp Sci & Cybernet, UA-02000 Kiev, Ukraine

[3] Univ Texas El Paso, Dept Math Sci, El Paso, TX 79968 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2019年 / 51卷 / 06期

关键词：

wave equation; Kelvin-Voigt damping; time-localized delay; well-posedness; exponential stability; singular limit; GLOBAL EXISTENCE; TIME DELAYS; EXPONENTIAL DECAY; STABILIZATION; BOUNDARY; STABILITY; BEHAVIOR; SYSTEMS; ENERGY; TERM;

D O I：

10.1137/18M1219308

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An initial-boundary value problem for a viscoelastic wave equation subject to a strong time-localized delay in a Kelvin-Voigt-type material law is considered. After transforming the equation to an abstract Cauchy problem on the extended phase space, a global well-posedness theory is established using the operator semigroup theory both in Sobolev-valued C-0- and BV-spaces. Under appropriate assumptions on the coefficients, a global exponential decay rate is obtained and the stability region in the parameter space is further explored using Lyapunov's indirect method. The singular limit tau -> 0 is studied with the aid of the energy method. Finally, a numerical example from a real-world application in biomechanics is presented.

引用

页码：4382 / 4412

页数：31

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