Global existence and exponential stability for a nonlinear thermoelastic Kirchhoff-Love plate

被引：16

作者：

Lasiecka, Irena ^{[1
,2
]}

Pokojovy, Michael ^{[1
,3
]}

Wan, Xiang ^{[4
]}

机构：

[1] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA

[2] Polish Acad Sci, IBS, Warsaw, Poland

[3] Karlsruhe Inst Technol, Dept Math, Karlsruhe, Germany

[4] Univ Virginia, Dept Math, Charlottesville, VA 22903 USA

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2017年 / 38卷

关键词：

Kirchhoff-Love plates; Nonlinear thermoelasticity; Hyperbolic-parabolic PDE systems; Global well-posedness; Classical solutions; Exponential stability;

D O I：

10.1016/j.nonrwa.2017.04.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study an initial boundary-value problem for a quasilinear thermoelastic plate of Kirchhoff & Love-type with parabolic heat conduction due to Fourier, mechanically simply supported and held at the reference temperature on the boundary. For this problem, we show the short-time existence and uniqueness of classical solutions under appropriate regularity and compatibility assumptions on the data. Further, we use barrier techniques to prove the global existence and exponential stability of solutions under a smallness condition on the initial data. It is the first result of this kind established for a quasilinear non-parabolic thermoelastic Kirchhoff & Love plate in multiple dimensions. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：184 / 221

页数：38

共 18 条

[1] ON THE PROBLEM OF VIBRATIONS OF NON-LINEAR-ELASTIC ELECTROCONDUCTIVE PLATES IN TRANSVERSE AND LONGITUDINAL MAGNETIC-FIELDS [J].

AMBARTSUMIAN, SA ;

BELUBEKIAN, MV ;

MINASSIAN, MM .

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 1984, 19 (02) :141-149

[2]

Ambartsumyan S. A., 1970, PROGR MAT SCI SERIES, V2

[3]

[Anonymous], MONOGRAPHS SURVEYS P

[4]

Chueshov I, 2010, KARMAN EVOLUTION EQU

[5] A structurally damped plate equation with Dirichlet-Neumann boundary conditions [J].

Denk, Robert ;

Schnaubelt, Roland .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (04) :1323-1353

[6]

Denk R, 2009, ADV DIFFERENTIAL EQU, V14, P685

[7] Analysis of nonlinear thermoelastic plate equations [J].

Hasanyan, D ;

Hovakimyan, N ;

Sasane, AJ ;

Stepanyan, V .

2004 43RD IEEE CONFERENCE ON DECISION AND CONTROL (CDC), VOLS 1-5, 2004, :1514-1519

[8] On well-posedness and small data global existence for an interface damped free boundary fluid-structure model [J].

Ignatova, Mihaela ;

Kukavica, Igor ;

Lasiecka, Irena ;

Tuffaha, Amjad .

NONLINEARITY, 2014, 27 (03) :467-499

[9]

Ilyushin A.A., 2004, UPRUGO PLASTIEESKIJE

[10]

Kato T., 1985, FERM LECT SCUOL NORM

← 1 2 →