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We focus on the general theory to the Cauchy problem for one dimensionalnonlinear wave equations with small initial data. In the general theory, we aimto obtain the lower bound estimate of the lifespan of classical solution. Inthis paper, we improve it in some case related to the combined effect, whichwas expected complete more than 30 years ago.

Improvement of the general theory for one dimensional nonlinear wave equations related to the combined effect