数学物理学报 ›› 2011, Vol. 31 ›› Issue (2): 273-288.

• 论文 •    下一篇

分布阻尼下非线性梁光滑解的存在性

贾超华1,2|冯德兴3   

  1. 1.北京航空航天大学 数学与系统科学学院 北京 100191|2.数学、信息与行为"教育部重点实验室 北京 100191|3.中国科学院数学与系统科学研究院系统所 北京 100190
  • 收稿日期:2008-12-25 修回日期:2010-10-20 出版日期:2011-04-25 发布日期:2011-04-25
  • 基金资助:

    国家自然科学基金(10626002)资助

The Existence of Smooth Solutions for a Nonlinear Beam with Distributed Damping

 JIA Chao-Hua1,2, FENG De-Xing3   

  1. 1.School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100191|2.LMIB of the Ministry of Education, Beijing 100191|3.Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190
  • Received:2008-12-25 Revised:2010-10-20 Online:2011-04-25 Published:2011-04-25
  • Supported by:

    国家自然科学基金(10626002)资助

摘要:

该文研究一个描述梁振动的非线性模型, 主要研究该模型在分布阻尼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: 非线性梁, 分布阻尼, 发展方程

Abstract:

This article is devoted to the study of the existence of local smooth solutions to a nonlinear beam with distributed damping. Applying the theory of evolution equations, we first show that related linear systems admit unique smooth solutions. Then some energy estimates for the linear systems are established. Finally we prove the existence of local smooth solutions to the nonlinear system by the fixed point argument.

Key words: Nonlinear beam, Distributed damping, Evolution equations

中图分类号: 

  • 93C20