Acta mathematica scientia,Series B ›› 1996, Vol. 16 ›› Issue (1): 51-59.

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CONSTRUCTION AND QUALITATIVE BEHAVIOR OF SOLUTIONS FOR A MODEL EQUATION FOR FLUID FLOW IN A PIPE

Li Yujian1, Hsiao Lin2   

  1. 1. Dept. of Neurobiology, Inst. of Biophysics, Academia Sinica, Beijing 100101, China;
    2. Inst. of Math., Academia Sinica, Beijing 100050, China
  • Received:1993-11-25 Revised:1994-12-05 Online:1996-03-25 Published:1996-03-25

Abstract: This paper investigates the following model equation:
vt-ux=0 ut+p(v)x+Avu=0
where A>0 and p'(v)<0.It proves that the equation admits a unique global discontinuous solution on in t > 0 class of piecewise continuous and piecewise smooth functions with a backward rarefaction wave and a forward shock wave under certain conditions.

Key words: Construction, qualitative behavior, rarefaction wave, shock wave

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