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Existence and energy decay of solutions for the Euler-Bernoulli viscoelastic equation with a delay

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成果类型:
期刊论文
作者:
Yang, Zhifeng*
通讯作者:
Yang, Zhifeng
作者机构:
[Yang, Zhifeng; Yang, ZF] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421002, Hunan, Peoples R China.
通讯机构:
[Yang, Zhifeng] H
Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421002, Hunan, Peoples R China.
语种:
英文
关键词:
Euler-Bernoulli viscoelastic equation;Energy decay;Internal feedbacks;Delay
期刊:
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
ISSN:
0044-2275
年:
2015
卷:
66
期:
3
页码:
727-745
基金类别:
Natural Science Foundation of Hunan Province, ChinaNatural Science Foundation of Hunan Province [14JJ7070]; Key Built Disciplines of Hunan Province [[2011]76]
机构署名:
本校为第一且通讯机构
院系归属:
数学与统计学院
摘要:
In this paper, we consider initial-boundary value problem of Euler–Bernoulli viscoelastic equation with a delay term in the internal feedbacks. Namely, we study the following equation $$u_{tt}(x,t)+ \Delta^2 u(x,t)-\int\limits_0^t g(t-s)\Delta^2 u(x,s){\rm d}s+\mu_1u_t(x,t)+\mu_2 u_t(x,t-\tau)=0 $$ together with some suitable initial data and boundary conditions in $${\Omega\times (0,+\infty)}$$ . For arbitrary real numbers μ 1 and μ 2, we prove that the above-mentioned model has a unique global solution under...

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