Acta mathematica scientia,Series A ›› 1983, Vol. 3 ›› Issue (2): 231-239.
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Abstract: We shall compare the solution of the Caucky problemut+(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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