The combined effect in one space dimension beyond the general theory for nonlinear wave equations

In this paper, we show the so-called "combined effect" of two different kinds of nonlinear terms for semilinear wave equations in one space dimension. Such a special phenomenon appears only in the case that the total integral of the initial speed is zero. It is remarkable that, including the combined effect case, our results on the lifespan estimates are partially better than those of the general theory for nonlinear wave equations.