APPROXIMATION CLOSE TO BLOW-UP TIME OF SOLUTIONS OF 2-DIMENSIONAL QUASI-LINEAR WAVE-EQUATIONS

For a general quasi-linear wave equation in two space dimensions and Cauchy data of size epsilon, we construct an approximate solution using the method of nonlinear geometric optics. Away from the blow up time, we obtain arbitrary accuracy near the light cone. Near the blow up time, we make explicit the behavior of the solution and of the error terms.