水动力型系统的Jordan型、抛物线性及型转变的其它特征
Jordan form, parabolicity and other features of change of type transition for hydrodynamic type systems
摘要：
讨论了两组分流体动力学型系统的型转变变化。结果表明，这些系统一般假设约旦形式（2 × 2约旦块）的过渡线与速端方程成为抛物型。讨论了双曲域到椭圆域过渡的条件。研究了Hamilton系统及其特殊的子类和方程，如无色散非线性Schroedinger方程、无色散Boussinesq方程、一维等熵气体动力学方程和非线性波方程。给出了无色散Boussinesq方程转捩线相交的数值结果。
英文摘要：
Changes of type transitions for the two-component hydrodynamic type systems are discussed. It is shown that these systems generically assume the Jordan form (with 2 X 2 Jordan block) on the transition line with hodograph equations becoming parabolic. Conditions which allow or forbid the transition from hyperbolic domain to elliptic one are discussed. Hamiltonian systems and their special subclasses and equations, like dispersionless nonlinear Schroedinger, dispersionless Boussinesq, one-dimensional isentropic gas dynamics equations and nonlinear wave equations are studied. Numerical results concerning the crossing of transition line for the dispersionless Boussinesq equation are presented too.
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