Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (4): 865-872.

• Articles •     Next Articles

A New Blow-up Condition for the Periodic Rod Equation

 LIU Yong-Ming1, ZHOU Yong2   

  1. 1.Department of Mathematics, East China Normal University, Shanghai 200241|2.Department of Mathematics, Zhejiang Normal University, Zhejiang Jinhua 321004
  • Received:2008-07-11 Revised:2009-08-22 Online:2010-07-25 Published:2010-07-25
  • Supported by:

    国家自然科学基金(10871071, 10971197)、上海市重点学科建设项目(B407)、上海市青年科技启明星跟踪计划(08QH14006)、教育部新世纪优秀人才支持计划(NCET-07-0299)和浙江省自然科学基金(R6090109)资助

Abstract:

In this paper, first the authors find optimal constants for a class of Sobolev inequalities by using Fourier expansion. This method is more direct and simple than the usual calculus of variation. Then, they establish a new blow-up condition for the period rod equation by the established inequality.

Key words: Rod equation, Inequality, Blow-up

CLC Number: 

  • 30C70
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