Semilinear wave equations of derivative type with characteristic weights in one space dimension

Abstract

In this paper, we investigate the lifespan estimates of classical solutions of the initial value problems for semilinear wave equations of derivative type with characteristic weights in one space dimension. Such equations provide us basic principles on extending the general theory for nonlinear wave equations to the non-autonomous case. In our results, two characteristic weights interact with each others and produce a different range of parameters on the global-in-time existence from the nonlinear terms of unknown function itself.