Acta mathematica scientia,Series B ›› 2000, Vol. 20 ›› Issue (4): 571-576.

• Articles • Previous Articles    

A NECESSARY AND SUFFICIENT CONDITION FOR GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO CAUCHY PROBLEM OF QUASILINEAR HYPERBOLIC SYSTEMS IN DIAGONAL FORM

 ZHENG Yong-Shu, LIU Fa-Gui   

  1. Department of Mathematics, Huaqiao University, Quanzhou, Fujian 362011, China North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450045, China
  • Received:1997-09-08 Online:2000-06-15 Published:2000-06-15
  • Supported by:

    Project supported by the NSF of China (19971062), the NSF of Fujian Province
    (A97020) and the NSF of Educational Committee of Henan Province

Abstract:

This article considers Cauchy problem for quasilinear hyperbolic systems in
diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem
admits a unique global classical solution on t  0 is obtained, and a sharp estimate of the
life span for the classical solution is given.

Key words: Cauchy problem, global classical solution, blow-up, life span

CLC Number: 

  • 35L60
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