National Institute of Technology, Kushiro College

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20012023

most citedTest function method for blow-up phenomena of semilinear wave equations and their weakly coupled systems

65 citations

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math.AP2022★ 4 cited

The lifespan estimates of classical solutions of one dimensional semilinear wave equations with characteristic weights

Shunsuke Kitamura, Hiroyuki Takamura, Kyouhei Wakasa

In this paper, we study the lifespan estimates of classical solutions for semilinear wave equations with characteristic weights and compactly supported data in one space dimension.…

math.AP2020

Critical exponent for the wave equation with a time-dependent scale invariant damping and a cubic convolution

Masahiro Ikeda, Tomoyuki Tanaka, Kyouhei Wakasa

In the present paper, we study the Cauchy problem for the wave equation with a time-dependent scale invariant damping $\frac{2}{1 + t} \partial_{t} v$ and a cubic convolution $(|x|^{-γ}…

math.AP2020★ 1 cited

Small data blow-up for the wave equation with a time-dependent scale invariant damping and a cubic convolution for slowly decaying initial data

Masahiro Ikeda, Tomoyuki Tanaka, Kyouhei Wakasa

In the present paper, we study the Cauchy problem for the wave equation with a time-dependent scale invariant damping, i.e. $\frac{2}{1 + t} \partial_{t} v$ and a cubic convolution $(|x|…

math.AP2019★ 21 cited

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

Takuto Imai, Masakazu Kato, Hiroyuki Takamura +1

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 dimensio…

math.AP2018

Finite time blowup of solutions to semilinear wave equation in an exterior domain

Motohiro Sobajima, Kyouhei Wakasa

We consider the initial-boundary value problem of semilinear wave equation with nonlinearity $∣ u ∣^{p}$ in exterior domain in $R^{N}$ $(N \geq 3)$ . Especially, the lifespan of b…

math.AP2018★ 8 cited

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

Masakazu Kato, Hiroyuki Takamura, Kyouhei Wakasa

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 asso…

math.AP2018★ 65 cited

Test function method for blow-up phenomena of semilinear wave equations and their weakly coupled systems

Masahiro Ikeda, Motohiro Sobajima, Kyouhei Wakasa

In this paper we consider the wave equations with power type nonlinearities including time-derivatives of unknown functions and their weakly coupled systems. We propose a framework…