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Kimitoshi Tsutaya

Publications and source records attributed to Kimitoshi Tsutaya.

6 recordsLinked to original sources
arXiv2025

Existence of solutions of semilinear wave equations with time-dependent propagation speed and time derivative nonlinearity

Consider wave equations with time derivative nonlinearity and time-dependent propagation speed which are generalized versions of the wave equations in the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime, the de Sitter spacetime and the anti-de Sitter space time. We show lower bounds of the lifespan of solutions as well as the global existence by providing an integrability condition on the propagation speed function, which is applicable to the nonlinear wave equation in the expanding FLRW spacetime including the de Sitter spacetime. We also prove that blow-up in a finite time occurs for the generalized form of the equation in contracting universes such as the anti-de Sitter spacetime, as well as upper bounds of the lifespan of blow-up solutions.

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arXiv2024

Appearance of Strauss-type exponent in semilinear wave equations with time-dependent speed of propagation

In this paper, blowup phenomenon for the semilinear wave equation with time-dependent speed of propagation and scattering damping is considered under the smallness of initial data. Our result contains small data blowup for sub-Strauss exponent for the simplest semilinear wave equation and also the one for semilinear generalized Tricomi equation. Key ingredient is so-called test function method (developed in Ikeda--Sobajima--Wakasa [10]) with a certain conservative quantity via a special solution with the Liouville--Green (or WKB) approximation.

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arXiv2021

Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat de Sitter spacetime. We show that blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as upper bounds of the lifespan of blow-up solutions.The blow-up condition is the same as in the accelerated expanding Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. We also show the same results for the space derivative nonlinear term.

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arXiv2021

On Glassey's conjecture for semilinear wave equations in Friedmann-Lemaître-Robertson-Walker spacetime

Consider nonlinear wave equations in the spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes. We show blow-up in finite time of solutions and upper bounds of the lifespan of blow-up solutions to give the FLRW spacetime version of Glassey's conjecture for the time derivative nonlinearity. We also show blow-up results for the space time derivative nonlinearity.

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arXiv2021

Blow up of solutions of semilinear wave equations in accelerated expanding Friedmann-Lemaître-Robertson-Walker spacetime

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat Friedmann-Lemaître-Robertson-Walker spacetimes. For the case of accelerated expansion, we show that blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as upper bounds of the lifespan of blow-up solutions. Comparing to the case of the Minkowski spacetime, we discuss how the scale factor affects the lifespan of blow-up solutions of the equation.

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