Long time existence of piecewise smooth progressing waves for semilinear wave equations (Q2640054)

We study the long time existence of piecewise smooth progressing waves solutions of a class of second order semilinear wave equations. We first obtain finite time blow-up results which in particular extend earlier work of Rauch. Then, under natural strict convexity assumptions, we obtain sharp lower bounds for the lifespan of outgoing piecewise smooth progressing waves; those bounds are of the same size as the ones obtained by Klainerman for smooth waves.