Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (6): 703-713.

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GLOBAL EXISTENCE AND BLOW-UP PHENOMENA OF CLASSICAL SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGH POROUS MEDIA

LIU Fa-gui1, KONG De-xing2   

  1. 1. Department of Mathematics and Information Sciences, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450008, P. R. China;
    2. Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200030, P. R. China
  • Received:2001-11-27 Revised:2003-12-08 Online:2004-06-18 Published:2004-06-18
  • Supported by:
    the National Natural Science Foundation of China(10001024);the Funds for Major State Basic Research Projects(2000077306)

Abstract: By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small’ solution.

2010 MSC Number: 

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