ON INTERACTION OF SHOCK AND SOUND WAVE （I）

This paper studies the interaction of shock and gradient wave (sound wave) of solutions to the system of inviscid isentropic gas dynamics as a model for the corresponding problems for nonlinear hyperbolic systems. The problem can be reduced to a boundary value problem in a wedged dormain, By using the method of constructing asymptotic solutions and Newton‘siteration process it is proved that if a weak shock hits a gradient wave, then the grandient wave will split into two gradient waves, while the shock continuses propagating. In this paper the author reduces the problem to a standard form and constructs asymptotic solution of the problem. The existence of the genuine solution will he given in the following paper.

ON INTERACTION OF SHOCK AND SOUND WAVE (I)

This paper studies the interaction of shock and gradient wave(sound wave) of solutions to the system of inviscid isentropicgas dynamics as a model for the corresponding problems fornonlinear hyperbolic systems. The problem can be reduced to aboundary value problem in a wedged domain. By using the method ofconstructing asymptotic solutions and Newton's iteration processit is proved that if a weak shock hits a gradient wave, then thegrandient wave will split into two gradient waves, while theshock continuses propagating. In this paper the author reducesthe problem to a standard form and constructs asymptotic solutionof the problem. The existence of the genuine solution will begiven in the following paper.