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

Abstract

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.

This version is already published in the publication in the journal, Communications on Pure and Applied Analysis. But it has an error in the citation on the result of the general theory in Introduction, which is related not to our resuts but to the title of this paper. So we place here its erratum at the end of this paper

References in corpus (3)

• The lifespan of classical solutions of semilinear wave equations with spatial weights and compactly supported data in one space dimension
• Semilinear wave equations of derivative type with spatial weights in one space dimension
• The combined effect in one space dimension beyond the general theory for nonlinear wave equations

Cited by in corpus (5)

• The combined effect in one space dimension beyond the general theory for nonlinear wave equations
• Blow-up of classical solutions of quasilinear wave equations in one space dimension
• The lifespan of classical solutions of one dimensional wave equations with semilinear terms of the spatial derivative
• The generalized combined effect for one dimensional wave equations with semilinear terms including product type
• The lifespan estimates of classical solutions of one dimensional semilinear wave equations with characteristic weights