arXiv subjects

Katsuaki Morisawa

Publications and source records attributed to Katsuaki Morisawa.

3 recordsLinked to original sources

arXiv2023

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.

math.AP↗

arXiv2022

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

This paper is devoted to the initial value problems for semilinear wave equations of derivative type with spatial weights in one space dimension. The lifespan estimates of classical solutions are quite different from those for nonlinearity of unknown function itself as the global-in-time existence can be established by spatial decay.

math.AP↗

arXiv2021

The lifespan of classical solutions of semilinear wave equations with spatial weights and compactly supported data in one space dimension

This paper studies initial value problems for semilinear wave equations with spatial weights in one space dimension. The lifespan estimates of classical solutions for compactly supported data are established in all the cases of polynomial weights. The results are classified into two cases according to the total integral of the initial speed.

math.AP↗