[1]刘 娟,蒲志林.一类带有非线性边界耗散的粘弹性方程解的存在性和能量估计[J].四川师范大学学报(自然科学版),2018,(05):578-585.[doi:10.3969/j.issn.1001-8395.2018.05.002]
 LIU Juan,PU Zhilin.Existence of Solutions and Energy Estimates for a Viscoelastic Equation with Nonlinear Boundary Dissipation[J].Journal of SichuanNormal University,2018,(05):578-585.[doi:10.3969/j.issn.1001-8395.2018.05.002]
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一类带有非线性边界耗散的粘弹性方程解的存在性和能量估计()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年05期
页码:
578-585
栏目:
基础理论
出版日期:
2018-06-15

文章信息/Info

Title:
Existence of Solutions and Energy Estimates for a Viscoelastic Equation with Nonlinear Boundary Dissipation
文章编号:
1001-8395(2018)05-0578-08
作者:
刘 娟 蒲志林
四川师范大学 数学与软件科学学院, 四川 成都 610066
Author(s):
LIU Juan PU Zhilin
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
非线性边界耗散 粘弹性方程 Faedo-Galerkin方法 能量衰减率
Keywords:
nonlinear boundary dissipation viscoelastic equation Faedo-Galerkin method energy decay rate
分类号:
O175.2
DOI:
10.3969/j.issn.1001-8395.2018.05.002
文献标志码:
A
摘要:
主要研究带有非线性边界耗散的粘弹性方程解的存在唯一性和能量衰减估计.首先,采用Faedo-Galerkin逼近方法证明全局解的存在唯一性并给出其变分形式; 其次,利用积分不等式和索伯列夫迹嵌入定理得到方程解的能量衰减率.
Abstract:
In this paper, we consider a viscoelastic equation with nonlinear boundary dissipation.We prove the existence and uniqueness of the solution by means of the Faedo-Galerkin method, and we obtain the explicit and general energy decay rate by making use of integral inequalities and Sobolev trace theorem.

参考文献/References:

[1] CHUESHOV I, ELLER M, LASIECKA I. On the attractor for a semilnear wave equation with critical exponent and nonlinear boundary dissipation[J]. Commum Partial Differ Eqns,2002,27(910):1901-1951.
[2] CAVALCANTI M M, CAVALCANTI V N D, LASIECKA I. Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction[J]. J Diff Eqns,2007,236(2):407-459.
[3] DAFERMOS C M. Asymptotic stability in viscoelasticity[J]. Archive for Rational Mechanics Analysis,1970,37(4):297-308.
[4] DAFERMOS C M. An abstract Volterra equation with applications to linear viscoelasticity[J]. J Diff Eqns,1970,7(7):554-569.
[5] MESSAOUDI S A. General decay of solutions of a viscoelastic equation[J]. J Math Anal Appl,2008,341(2):1457-1467.
[6] AASSILA M, CAVALCANTI M M. Existence and uniform decay of the wave equation with nonlinear boundary damping and boumdary memory source term[J]. Calculus of Variations Partial Diff Eqns,2002,15(2):155-180.
[7] CAVALCANTI M M, CAVALCANTI V N D, FILHOJ S P, et al. Existence and uniform decay rates for viscoelastic problems with nonlocal boundary damping[J]. Differ Integral Eqns,2001,14(1):85-116.
[8] MESSAOUDI S A, MUSTAFA M I. On convexity for energy decay rates of a viscoelastic equation with boundary feedback[J]. Nonl Anal,2010,72(72):3602-3611.
[9] WU S T, CHEN H F. Uniform decay of soluntions for a nonlinear viscoelastic wave equation with boundary disspation[J]. J Function and Spaces Appl,2012,42(88):1-17.
[10] MIGORSKI S. Evolution hemivariational inequality for a class of dynamic viscoelastic nonmonotone frictional contact problems[J]. Comput Math with Appl,2006,52(5):677-698.
[11] MESSAOUDI S A, TATAR N E. Global existence and uniform stability of solutions for a quasilinear viscoelastic problem[J]. Math Methods in the Applied Sciences,2007,30(6):665-680.
[12] RIVERA J E M, ANDRADE D. Exponential decay of non-linear wave equation with a viscoelastic boundary condition[J]. Math Methods in the Applied Sciences,2000,23(1):41-61.
[13] NASCIMENTO F A F, LASIECKA I, CAVALCANTI V N D, et al. Intrinsic decay rate estimates for the wave equation with competing viscoelastic and frictional dissipative effects[J]. Discrete and Continuous Dynamical Systems,2014,B19(7):1987-2011.
[14] BERRIMI S, MESSAOUDI S A. Existence and decay of solutions of a viscoelastic equation with a nonlinear source[J]. Nonl Anal,2006,64(10):2314-2331.

备注/Memo

备注/Memo:
收稿日期:2016-12-06 接受日期:2017-03-04
基金项目:四川省科技计划项目(2015JY0125)
*通信作者简介:蒲志林(1963—),男,教授,主要从事无穷维动力系统理论的研究,E-mail:Puzhiilin908@sina.com
更新日期/Last Update: 2018-04-15