Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (2): 273-288.

• Articles •     Next Articles

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

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

CLC Number: 

  • 93C20
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