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边界输入输出结构下非线性梁光滑解的存在性(英文)
引用本文:贾超华. 边界输入输出结构下非线性梁光滑解的存在性(英文)[J]. 数学进展, 2010, 0(2)
作者姓名:贾超华
作者单位:北京航空航天大学数学与系统科学学院数学、信息与行为教育部重点实验室;
基金项目:supported by the NSFC(No.10626002)
摘    要:本文研究一个描述梁振动的非线性模型,其非线性由物理条件(Hooke律)导致,主要研究该模型在边界输入输出结构下局部光滑解的存在性.首先应用发展方程理论证明相关线性系统存在光滑解,然后由一系列能量估计结合不动点定理证明所考察的非线性系统局部光滑解的存在性.

关 键 词:Bernoulli-Euler梁  非线性梁  边界输入输出  发展方程  

The Existence of Smooth Solutions for a Nonlinear Beam With Boundary Input and Output
JIA Chaohua. The Existence of Smooth Solutions for a Nonlinear Beam With Boundary Input and Output[J]. Advances in Mathematics(China), 2010, 0(2)
Authors:JIA Chaohua
Affiliation:JIA Chaohua (School of Mathematics , Systems Science,Beijing University of Aeronautics , Astronautics,LMIB of the Ministry of Education,Beijing,100191,P.R.China)
Abstract:In this article a dynamical system modeling the bending vibrations of a quasilinear beam is considered,where the nonlinearity comes from Hooke's law.We are concerned with the existence of local smooth solutions to this quasi-linear beam with boundary input and output.Applying the evolution system theory,we first show that a related linear system admits a unique smooth solution.Then some energy estimates for the linear system are established. Finally the existence of local smooth solutions to the quasi-linea...
Keywords:Bernoulli-Euler beam  nonlinear beam  boundary input and output  evolution system  
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