8 citations · 14 across the 11 of their papers we have counts for
11 papers
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…
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…
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…
Blow-up of solutions to semilinear wave equations with spatial derivatives
Kerun Shao, Hiroyuki Takamura, Chengbo Wang
For small-amplitude semilinear wave equations with power type nonlinearity on the first-order spatial derivative, the expected sharp upper bound on the lifespan of solutions is obt…
A blow-up result for the semilinear Euler-Poisson-Darboux-Tricomi equation with critical power nonlinearity
Ning-An Lai, Alessandro Palmieri, Hiroyuki Takamura
In this paper, we prove a blow-up result for a generalized semilinear Euler-Poisson-Darboux equation with polynomially growing speed of propagation, when the power of the semilinea…
Blow-up of classical solutions of quasilinear wave equations in one space dimension
Yuki Haruyama, Hiroyuki Takamura
This paper studies the upper bound of the lifespan of classical solutions of the initial value problems for one dimensional wave equations with quasilinear terms of space-, or time…
Recent developments on the lifespan estimate for classical solutions of nonlinear wave equations in one space dimension
Hiroyuki Takamura
In this paper, we overview the recent progresses on the lifespan estimates of classical solutions of the initial value problems for nonlinear wave equations in one space dimension.…
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…