Acta mathematica scientia,Series A ›› 1983, Vol. 3 ›› Issue (2): 231-239.

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STUDY OF THE GLOBAL SOLUTIONS FOR A NONLINEAR HYPERBOLIC SYSTEM

  

  1. Institute of Systems Science, Academia Senica
  • Received:1983-02-20 Online:1983-06-26 Published:1983-06-26

Abstract: We shall compare the solution of the Caucky problem
ut+(v-1)x=0 vt-ux=0 (1.1)
(u,v)(0,x)=(u0(x),v0(x)) (1.2) with the solution of the corresponding Riemann problem (1.1) with the initial data
(u,v)(0,x)=(u-,v-) for x<0 (u+,v+) for x>0 (1.2)' in the whole t>0 half plane.The system of equations (1.1) is the mathematical modol for isentropic gas dynamics with adiabatic exponent x=1 Here v is tlie specific volume v=(1)/ρ,ρ is the density and u is the speed of the gas (u,v)=limx→∓∞(u0(x),v0(x)).

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