ASYMPTOTIC EQUATIONS FOR CONSERVATION-LAWS OF MIXED TYPE

We derive canonical asymptotic equations for weakly nonlinear solutions of conservation laws of mixed type. When two real wave speeds coalesce and become complex, we obtain the transonic small disturbance equation which changes type from hyperbolic to elliptic. When the coefficient of the nonlinear term in the transonic small disturbance equation vanishes, we derive cubically nonlinear 2 x 2 asymptotic equations. These include canonical equations which are parabolic on a line in state space and strictly hyperbolic away from this line.