带非线性阻尼的粘弹方程解的整体存在性和一致衰减性
Global Existence and Uniform Decay of Solutions to Viscoelastic Equations with Nonlinear Damping
摘要
研究带有非线性阻尼的粘弹方程,得到了弱解整体存在性和一致指数衰减性.
This paper investigates the viscoelastic equations with nonlinear damping. The global existence of weak solution and uniform decay of the energy are obtained.
出处
《数学年刊（A辑）》
CSCD
北大核心
2009年第1期31-42,共12页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.10771032)
江苏省自然科学基金(No.BK2006088)
江苏省普通高校研究生科研创新计划(No.CX08B_001Z)资助的项目.
关键词
整体存在性
指数衰减性
粘弹方程
非线性阻尼
Global existence, Exponential decay, Viscoelastic equations, Nonlinear damping
参考文献13
-
1Cavalcanti M. M., Domingos Cavalcanti V. N. and Ferreira J., Existence and uniform decay for a nonlinear viscoelastic equation with strong damping [J], Math. Meth. Appl. Sci., 2001, 24:1043-1053.
-
2Messaoudi S. A. and Tatar N., Exponential and polynomial decay for a quasilinear viscoelastic equation [J], Nonlinear Anal., 2008, 68:785 793.
-
3Messaoudi S. A. and Tatar N., Global existence and uniform decay of solutions for a quasilinear viscoelastic problem [J], Math. Meth. Appl. Sci., 2007, 30:665 680.
-
4Cavalcanti M. M., Domingos Cavalcanti V. N. and Soriano J. A., Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping [J], Elect. Y. Differ. Equ., 2002, 44:1-14.
-
5Berrimi S. and Messaoudi S. A., Exponential decay of solutions to a viscoelastic equation withnonlinear localized damping [J], Elect. J. Differ. Equ., 2004, 88:1-10.
-
6Messaoudi S. A., Blow-up and global existence in a nonlinear viscoelastic wave equation [J], Math. Nach., 2003, 260:58-66.
-
7Messaoudi S. A., Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation [J], J. Math. Anal. Appl., 2006, 320:902-915.
-
8Andrade D., Fatori L. H. and Rivera J. M., Nonlinear transmission problem with a dissipative boundary condition of memory type [J], Elect. J. Differ. Equ., 2006, 53:1- 16.
-
9Berrimi S. and Messaoudi S. A., Existence and decay of solutions of a viscoelastic equation with a nonlinear source [J], Nonlinear Anal., 2006, 64:2314-2331.
-
10Cavalcanti M. M., Domingos Cavalcanti V. N., Ma T. F. and Soriano J. A., Global existence and asymptotic stability for viscoelastic problems [J], Differ. Integral. Equ., 2002, 15:731-748.
-
1马志勇,罗琳.带有记忆的粘弹方程解的整体存在性[J].上海第二工业大学学报,2011,28(2):103-105. 被引量：1
-
2张志平,姬小龙.一类非线性粘弹方程[J].系统科学与数学,2009,29(12):1622-1630.
-
3秦玉明,胡阳艳,刘震宇,袁亚波,安晶晶,周奥.具有非线性阻尼粘弹方程的一致吸引子(Ⅰ)(英文)[J].河南大学学报（自然科学版）,2014,44(3):253-260. 被引量：2
-
4阳志锋.具边界反馈时滞的粘弹方程的能量衰减(英文)[J].应用数学,2015,28(1):1-9. 被引量：1
