期刊论文

中文

应用数学

1001-9847

2015

28

1

1-9

10.13642/j.cnki.42-1184/o1.2015.01.001

(14JJ7070):Supported by the Natural Science Foundation of Hunan Province (Hengyang Normal University,2011):and the Key Built Disciplines of Hunan Province-Operations Research and Control Theory

本校为第一机构

考虑如下具边界反馈时滞的粘弹方程{utt(x,t)-△u(x,t) + ∫t0(-s)△u(x,s)ds =0,x ∈ Ω,t ＞ 0,u(x,t) =0,x ∈ Γ0,t ＞ 0,(e)u/(e)v =∫t0g(t-s) (e)/(e)vu(s)ds-μ1ut(x,t)-μ2ut(x,t-τ),x∈ Γ1,t＞0,u(x,0) =u0(x),ut(x,0) =u1(x),x ∈ Ω,ut(x,t-τ) =f0(x,t-τ),x ∈ Ω,0 ＜ t＜ τ,}其中Ω∈Rn(n≥1)是具C2类边界(e)Ω的有界域.此外,g是所谓的“记忆核”,μ1,μ2是两个实数,τ为时滞.在假设|μ2|＜μ1下,通过构造合适的Lyapunov函数,证明上述问题能量的一般衰减性,使得指数型衰减和多项式衰减仅仅是其特殊情况.

We consider a viscoelastic wave equation with a delay term in the boundary feedback; namely,we study the following problem where ? ∈ (n≥1） be a regular and bounded domian with a boundary a? of class C~2.Moreover,g is so-called "memory kernel",μ_1,μ_2 are two real coefficients which are not necessarily positive,and Γ represents the time delay.Under the restriction |μ_2|