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Masakazu Kato

Publications and source records attributed to Masakazu Kato.

6 recordsLinked to original sources
arXiv2026

A revisit via slicing method on a quadratic semilinear wave equation in two space dimensions

In this paper, we are focusing on the proof of the blow-up result for a quadratic semilinear wave equation in two space dimensions. There is a logarithmic loss in estimating the lifespan of classical solutions if the 0th moment of the initial speed does not vanish. This result is already known with almost sharp constants. But in order to have a direct application to numerical analysis, we show a simple proof by iteration argument of point-wise estimate of the solution with the slicing technique.

math.AP↗
arXiv2022

Critical exponent for nonlinear wave equations with damping and potential terms

The aim of this paper is to determine the critical exponent for the nonlinear wave equations with damping and potential terms of the scale invariant order, by assuming that these terms satisfy a special relation. We underline that our critical exponent is different from the one for related equations such as the nonlinear wave equation without lower order terms, only with a damping term, and only with a potential term. Moreover, we study the effect of the decaying order of initial data at spatial infinity. In fact, we prove that not only the lower order terms but also the order of the initial data affects the critical exponent, as well as the sharp upper and lower bounds of the maximal existence time of the solution.

math.AP↗
arXiv2020

The lifespan of solutions of semilinear wave equations with the scale-invariant damping in two space dimensions

In this paper, we study the initial value problem for semilinear wave equations with the time-dependent and scale-invariant damping in two dimensions. Similarly to the one dimensional case by Kato, Takamura and Wakasa in 2019, we obtain the lifespan estimates of the solution for a special constant in the damping term, which are classified by total integral of the sum of the initial position and speed. The key fact is that, only in two space dimensions, such a special constant in the damping term is a threshold between "wave-like" domain and "heat-like" domain. As a result, we obtain a new type of estimate especially for the critical exponent.

math.AP↗
arXiv2019

The lifespan of solutions of semilinear wave equations with the scale-invariant damping in one space dimension

The critical constant of time-decaying damping in the scale-invariant case is recently conjectured. It also has been expected that the lifespan estimate is the same as for the associated semilinear heat equations if the constant is in the \heat-like" domain. In this paper, we point out that this is not true if the total integral of the sum of initial position and speed vanishes. In such a case, we have a new type of the lifespan estimates which is closely related to the non-damped case in shifted space dimensions.

math.AP↗