Behavior of the Overtaking Problem for Isentropic Gas Dynamics Equations with Polytropic Gas in Exponent γ=3
The entropy weak solution of the isentropic gas dynamics system has the important background of physics and mechanics, and the study on the interaction of nonlinear elementary wave not only had direct mechanics significance, but also was an effective method to clarify the structure of the weak solution. We explored the overtaking problem of the centred rarefaction wave and the shock wave for isentropic gas dynamics system with polytropic gas in γ=3. By using Riemann invariants, the characteristic method and convexity analysis for the envelope of compression waves, we clarified the physical state after interaction for the overtaking problem in the interaction location, and proved that the locally structure of the entropy weak solution was piecewise smooth.
T. Pan "Behavior of the Overtaking Problem for Isentropic Gas Dynamics Equations with Polytropic Gas in Exponent γ=3", Applied Mechanics and Materials, Vols. 52-54, pp. 405-410, 2011