Blow-up of classical solutions of quasilinear wave equations in one space dimension

This paper studies the upper bound of the lifespan of classical solutions of the initial value problems for one dimensional wave equations with quasilinear terms of space-, or time-derivatives of the unknown function. The results are same as those of the semilinear case. But it is quite meaningful to consider this kind of problems for the purpose to cover the optimality of the general theory for nonlinear wave equations by many model equations as far as possible.