BOUNDARY BEHAVIOR OF SOLUTIONS OF A CLASS OF GENUINELY NONLINEAR HYPERBOLIC SYSTEMS

We study the set of boundary singularities of arbitrary classical solutions of genuinely nonlinear $2\times2$ planar hyperbolic systems of the form $D_kR_k=0$, where $D_k$ denotes differentiation in the direction $e^{i\theta_k(R_1,R_2)}$, $k=1,2$, and where the defining functions $\theta_k$ satisfy (i) $\theta_2=\theta_1+\frac{\pi}{2}$, and (ii) $A\leq|\frac{\partial\theta_k(R)}{\partial R_k}| \leq B$, for all $R\in\mathbb{R}^2$, $k=1,2$, for some positive constants $A,B$. We show that for any system of this kind there is a $\tau