GENERAL DECAY RATE ESTIMATES FOR VISCOELASTIC WAVE EQUATION WITH VARIABLE COEFFICIENTS
查看参考文献20篇
文摘
|
The authors study decay properties of solutions for a viscoelastic wave equation with variable coefficients and a nonlinear boundary damping by the differential geometric approach. |
来源
|
Journal of Systems Science and Complexity
,2014,27(5):836-852 【核心库】
|
DOI
|
10.1007/s11424-014-1056-x
|
关键词
|
Energy decay
;
nonlinear boundary damping
;
Riemannian metric
;
viscoelastic wave equation
|
地址
|
1.
School of Mathematical Sciences, Shanxi University, Taiyuan, 030006
2.
Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Key Laboratory of Control and Systems, Chinese Academy of Sciences, Beijing, 100190
|
语种
|
英文 |
文献类型
|
研究性论文 |
ISSN
|
1009-6124 |
学科
|
数学 |
基金
|
国家自然科学基金
;
the Excellent PhD Adviser Program of Beijing
|
文献收藏号
|
CSCD:5314371
|
参考文献 共
20
共1页
|
1.
Cavalcanti M M. Existence and uniform decay rates for viscolelastic problems with nonlinear boundary damping.
Differential and Integral Equations,2001,14(1):85-116
|
CSCD被引
5
次
|
|
|
|
2.
Cavalcanti M M. General decay rate estimates for viscoelastic dissipative systems.
Nonlinear Analysis: Theory, Methods & Applications,2008,68:177-193
|
CSCD被引
6
次
|
|
|
|
3.
Messaoudi S A. On convexity for energy decay rates of a viscoelastic equation with boundary feedback.
Nonlinear Analysis: Theory, Methods & Applications,2010,72:3602-3611
|
CSCD被引
5
次
|
|
|
|
4.
Chai S G. Boundary stabilization of wave equation with variable coefficients and memory.
Differential and Integral Equations,2004,17:669-680
|
CSCD被引
1
次
|
|
|
|
5.
Chai S G. Boundary stabilization of the transmission of wave equations with variable coefficients.
Chinese Ann. Math. (Ser. A),2005,26(5):605-612
|
CSCD被引
1
次
|
|
|
|
6.
Feng S J. Boundary stabilization of wave equations with variable coefficients.
Science in China (Ser. A),2001,44(3):345-350
|
CSCD被引
5
次
|
|
|
|
7.
Guo B Z. On exponential stability of a semilinear wave equation with variable coefficients under the nonlinear boundary feedback.
Nonlinear Analysis: Theory, Methods & Applications,2009,71:5961-5978
|
CSCD被引
2
次
|
|
|
|
8.
Cavalcanti M M. Uniform stabilization of the damped Cauchy- Ventcel problem with variable coefficients and dynamic boundary conditions.
Journal of Mathematical Analysis and Applications,2007,328:900-930
|
CSCD被引
4
次
|
|
|
|
9.
Yao P F. On the observability inequalities for exact controllability of wave equations with variable coefficients.
SIAM J. Control Optim,1999,37:1568-1599
|
CSCD被引
25
次
|
|
|
|
10.
Martinez P. A new method to obtain decay rate estimates for dissipative systems.
ESAIM Control Optim. Calc. Var,1999,4:419-444
|
CSCD被引
9
次
|
|
|
|
11.
Martinez P. A new method to obtain decay rate estimates for dissipative systems with localized damping.
Rev. Mat. Complutense,1999,12(1):251-283
|
CSCD被引
1
次
|
|
|
|
12.
Cavalcanti M M. Frictional versus viscoelastic damping in a semilinear wave equation.
SIAM J. Control Optim,2003,42(4):1310-1324
|
CSCD被引
19
次
|
|
|
|
13.
Haraux A.
Two Remarks on Dissipative Hyperbolic Problems, Research Notes in Mathematics, vol.122,1985:161-179
|
CSCD被引
1
次
|
|
|
|
14.
Komornik V.
Exact Controllability and Stabilization: The Multiplier Method,1994
|
CSCD被引
7
次
|
|
|
|
15.
Lasiecka I. Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping.
Differential and Integral Equations,1993,6(3):507-533
|
CSCD被引
10
次
|
|
|
|
16.
Lions J L.
Non-Homogeneous Boundary Value Problem and Applications, vol. I,1972
|
CSCD被引
1
次
|
|
|
|
17.
Renardy M.
Mathematical Problems in Viscoelasticity, Pitman Monographs and Surveys in Pure and Appl. Math., vol. 35,1987
|
CSCD被引
1
次
|
|
|
|
18.
Wu H.
An Introduction to Riemannian Geometry, (in Chinese),1989
|
CSCD被引
1
次
|
|
|
|
19.
Yao P F. Observability inequalities for shallow shells.
SIAM J. Control Optim,2000,38:1729-1756
|
CSCD被引
9
次
|
|
|
|
20.
Zuazua E. Uniform stabilization of the wave equation by nonlinear boundary feedback.
SIAM J. Control Optim,1990,28:466-478
|
CSCD被引
8
次
|
|
|
|
|