Improvement of the general theory for one dimensional nonlinear wave equations related to the combined effect (2308.02174v2)

Abstract: We focus on the general theory to the Cauchy problem for one dimensional nonlinear wave equations with small initial data. In the general theory, we aim to obtain the lower bound estimate of the lifespan of classical solution. In this paper, we improve it in some case related to the combined effect, which was expected complete more than 30 years ago.