Abstract:
The Goursat problem of a mixed type equation , P≥ 0, is considered. At the ends of its supports we have P=0, which means it is degenerate hyperbolic. We prove the global existence of a smooth solution to the degenerate Goursat problem up to a boundary where P=0. This problem comes from the expansion of a wedge of gas with constant velocity into vacuum, in two-dimensional pressure-gradient equations in gas dynamics, where P is the pressure and P=0 means vacuum.
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Accepted June 16, 2000¶Published online December 6, 2000
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Dai, Z., Zhang, T. Existence of a Global Smooth Solution¶for a Degenerate Goursat Problem¶of Gas Dynamics. Arch. Rational Mech. Anal. 155, 277–298 (2000). https://doi.org/10.1007/s002050000113
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DOI: https://doi.org/10.1007/s002050000113