| 变系数Euler-Bernoulli梁振动发展系统的存在性 |
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| 引用本文： | 武洁琼,陈发师. 变系数Euler-Bernoulli梁振动发展系统的存在性[J]. 应用泛函分析学报, 2003, 5(4): 307-310 |
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| 作者姓名： | 武洁琼 陈发师 |
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| 作者单位： | 1. 山西大学数学系,山西,太原,030006
2. 山西财经大学数学系,山西,太原,030006 |
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| 基金项目： | Supported by N SFC( 6 0 174 0 0 7) |
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| 摘 要： | 讨论变系数Euler-Bernoulli梁振动系统{uu(x,t) η(t)uxxxx(x,t)=0,0＜x＜1,0≤t≤T u(0,t)=ux(0,t)=0,0≤t≤t -uxxx(1,t) muu(1,t)=-αu1(1,t) βuxxx(1,t),0≤t≤T uxt(1,t) =-γuxx(1,t),0≤t≤t u(x,0)=u1(x),u1(x,0),0≤x≤1证明了该系统产生一个发展系统．
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| 关 键 词： | 变系数 发展系统 存在性 证明 振动系统 |
Existence of Evolution System of Euler-Bernoulli Beam with Variable Coefficient |
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| WU Jie-qiong,CHEN Fa-shi. Existence of Evolution System of Euler-Bernoulli Beam with Variable Coefficient[J]. Acta Analysis Functionalis Applicata, 2003, 5(4): 307-310 |
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| Authors: | WU Jie-qiong CHEN Fa-shi |
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| Abstract: | A flexible structure consisting of Euler-Bernoulli beam with a variable coefficient described by utt(x,t) +-η(t)uxxxx (x,t)=0, 0＜x＜1, 0≤t≤T u(0,t) = ux(0,t) = 0, 0 ≤ t ≤ T { - uxxx(1,t) +mutt(1,t) =- aut(1,t) + βuxxxt(1,t), 0≤t≤T (1) uxt(1,t) =-γuxx(1,t), 0≤t≤T u(x,0) =u1(x), ut(x,0) =u2(x), 0≤x≤ 1 is considered. We prove that the system generate an evolution system when η(t) is a continuous function and η(t) ∈∨ [0,T], 0＜η0≤η(t)≤M. |
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| Keywords: | C_0 contraction semigroup stable family evolution system |
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