GEVREY CLASS OF LOCALLY DISSIPATIVE EULER-BERNOULLI BEAM EQUATION

被引：4

作者：

Gomez Avalos, G. ^{[1
]}

Rivera, J. Munoz ^{[2
,3
]}

Liu, Z. ^{[4
]}

机构：

[1] Univ Andres Bello, Dept Matemat, Autopista Concepcion Tal 7100, Talcahuano, Chile

[2] Univ Bio Bio, Dept Matemat, Concepcion, Chile

[3] Natl Lab Sci Computat, Rio De Janeiro, Brazil

[4] Univ Minnesota, Math & Stat, Duluth, MN 55812 USA

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2021年 / 59卷 / 03期

关键词：

C-0-semigroup; thermoviscoelasticity; viscoelasticity; Kelvin-Voigt damping; differentiability; Gevrey class; exponential stability; EXPONENTIAL DECAY; POLYNOMIAL DECAY; ELASTIC-SYSTEMS; ENERGY; STABILIZATION; STABILITY; WAVES;

D O I：

10.1137/20M1312800

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We study the semigroup associated to the Euler-Bernoulli beam equation with localized (discontinuous) dissipation. We assume that the beam is composed of three components: elastic, viscoelastic of Kelvin-Voigt type, and thermoelastic parts. We prove that this model generates a semigroup of Gevrey class that in particular implies the exponential stability of the model. To our knowledge, this is the first positive result giving increased regularity for the Euler-Bernoulli beam with localized damping.

引用

页码：2174 / 2194

页数：21

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