| 摘 要： | § 1. Introduction The Riemann problem is the most basic problem for both analytical theory and numerical computation of nonlinear hyperbolic conservation laws. B. Riemann suggested and solved it for one dimensional isentropic flow in 1860. A lot of work have been done for 1-D case since 1940's. For 2-D scalar conservation law, it has been solved by Wagner and Zhang and Zheng. For 2-D system of Euler equations in gas dynamios, after some demonstration and analysis with characteristic method in both physics and phase spaces a set of conjectures on the structure of solutions have been formulated by Zhang and Zheng. To approach the proof of the conjectures, we consider a 2×2 system first. In the present paper we discuss the following system:
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