9 papers
A revisit on the critical blow-up for semilinear wave equations in low space dimensions with slicing method
Hiroyuki Takamura
In this reviewing paper, we are interested in the proof of estimating the lifespan of classical solutions of semilinear wave equations with the critical exponent from above especia…
A revisit via slicing method on a quadratic semilinear wave equation in two space dimensions
Masakazu Kato, Hiroyuki Takamura, Kyouhei Wakasa
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 li…
Lifespan estimate for one dimensional wave equation with semilinear terms of spatial derivative
Ning-An Lai, Cui Ren, Takiko Sasaki +1
This paper studies the upper and lower bounds of the lifespan for the classical solutions to the initial value problems of one dimensional wave equations with non-autonomous semili…
Blow-up of solutions to the Euler-Poisson-Darbox equation with critical power nonlinearity
Mengting Fan, Ning-An Lai, Hiroyuki Takamura
In our recent precious work, we established the finite time blow up result and upper bound of lifespan estimate to the singular Cauchy problem of semilinear Euler-Poisson-Darboux e…
Slicing method for nonlinear integral inequalities related to critical nonlinear wave equations
Takiko Sasaki, Kerun Shao, Hiroyuki Takamura
This paper is devoted to a simple and short proof on the sharp upper bound of lifespan of classical solutions to wave equations with the critical power nonlinearities of spatial de…
Note on the existence of classical solutions of derivative semilinear models for one dimensional wave equation
Yuki Haruyama, Takiko Sasaki, Hiroyuki Takamura
This note is a supplement with a new result to the review paper by Takamura [13] on nonlinear wave equations in one space dimension. We are focusing here to the long-time existence…