边界输入输出结构下非线性梁光滑解的存在性(英文)  

The Existence of Smooth Solutions for a Nonlinear Beam With Boundary Input and Output

作　　者：贾超华[1] 

机构地区：[1]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,北京100191

出　　处：《数学进展》2010年第2期187-202,共16页Advances in Mathematics（China）

基　　金：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.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-linear system is shown through fixed point arguments.

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

分 类 号：O231.4[理学—运筹学与控制论]