Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (4): 1122-1132.

• Articles • Previous Articles     Next Articles

On the Existence of Weak Solutions for Nonlinear Schr\"{o}dinger-Klein-Gordon Equations

 SHI Qi-Hong1, WANG Shu2, WANG Chang-Wei2,3   

  1. 1.Fundamental Department, Hebei Finance University, Hebei Baoding 071051|2.College of Applied Sciences, Beijing University of Technology, Beijing 100124|3.College of Mathematics and Physics, Chongqing University of Posts and Telecommunications,
    Chongqing 400065
  • Received:2009-10-08 Revised:2010-09-10 Online:2011-08-25 Published:2011-08-25
  • Supported by:

    国家自然科学基金(10771009)、北京市自然科学基金(1085001)、北京市属高校人才强教深化计划学术创新人才基金、北京市教委自然科学基金和重庆市自然科学基金(2008BB7415)资助

Abstract:

In this paper, the Cauchy problem to the nonlinear Schr\"{o}dinger-Klein-Gordon equations in 3+1 time-space is studied. Under certain assumptions on nonlinear terms and the initial data, the existence of global weak solutions is obtained by the viscous method and the energy method combined with the compactness arguments.

Key words: Nonlinear, Schr\"{o}dinger-Klein-Gordon, Approximate system, Global solution

CLC Number: 

  • 35B25
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