93 citations · 240 across the 24 of their papers we have counts for
24 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…
Threshold-crossing estimates for time-weighted discrete semilinear wave equations
Koji Wada, Kyouhei Wakasa
In this paper, we consider the initial value problem for a discrete semilinear wave equation with a time weight, obtained by the standard centered finite-difference scheme. The sol…
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.…
On the critical decay for the wave equation with a cubic convolution in 3D
Tomoyuki Tanaka, Kyouhei Wakasa
We consider the wave equation with a cubic convolution in three space dimensions. Here, and stands for the convolution in the space…
Lifespan estimates for -dimensional semilinear wave equations in asymptotically Euclidean exterior domains
Ning-An Lai, Mengyun Liu, Kyouhei Wakasa +1
In this paper we study the initial boundary value problem for two-dimensional semilinear wave equations with small data, in asymptotically Euclidean exterior domains. We prove that…
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 and a cubic convolution $(|x|^{-γ}…
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. and a cubic convolution $(|x|…
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…
Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass
Masahiro Ikeda, Ziheng Tu, Kyouhei Wakasa
In the present paper, we study small data blow-up of the semi-linear wave equation with a scattering dissipation term and a time-dependent mass term from the aspect of wave-like be…
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 in exterior domain in . Especially, the lifespan of b…
Critical exponent for nonlinear damped wave equations with non-negative potential in 3D
Vladimir Georgiev, Hideo Kubo, Kyouhei Wakasa
We are studying possible interaction of damping coefficients in the subprincipal part of the linear 3D wave equation and their impact on the critical exponent of the corresponding…
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…
On the blow-up for critical semilinear wave equations with damping in the scattering case
Kyouhei Wakasa, Borislav Yordanov
We consider the Cauchy problem for semilinear wave equations with variable coefficients and time-dependent scattering damping in , where . It is expected tha…
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…
Blow-up of solutions to critical semilinear wave equations with variable coefficients
Kyouhei Wakasa, Borislav Yordanov
We verify the critical case of Strauss' conjecture (1981) concerning the blow-up of solutions to semilinear wave equations with variable coefficients in ,…
Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent
Ning-An Lai, Hiroyuki Takamura, Kyouhei Wakasa
The blow-up for semilinear wave equations with the scale invariant damping has been well-studied for sub-Fujita exponent. However, for super-Fujita exponent, there is only one blow…
The sharp lower bound of the lifespan of solutions to semilinear wave equations with low powers in two space dimensions
Takuto Imai, Masakazu Kato, Hiroyuki Takamura +1
This paper is devoted to a proof of the conjecture in Takamura(2015) on the lower bound of the lifespan of solutions to semilinear wave equations in two space dimensions. The resul…
Global Regularity for Supercritical Nonlinear Dissipative Wave Equations in 3D
Kyouhei Wakasa, Borislav Yordanov
The nonlinear wave equation is shown to be globally well-posed in the Sobolev spaces of radially symmetric functions $H^k_{\rm rad}({\bf R}^3)\times H…
The lifespan of solutions to wave equations with weighted nonlinear terms in one space dimension
Kyouhei Wakasa
In this paper, we consider the initial value problem for nonlinear wave equation with weighted nonlinear terms in one space dimension. Kubo & Osaka & Yazici(2013) studied global so…
Blow-Up of Positive Solutions to Wave Equations in High Space Dimensions
Hiroyuki Takamura, Mohammad Rammaha, Hiroshi Uesaka +1
This paper is concerned with the Cauchy problem for the semilinear wave equation: $u_{tt}-Δu=F(u) \ \mbox{in} \ R^n\times[0, \infty)$, where the space dimension , $F(u)=|u…
Global existence for semilinear wave equations with the critical blow-up term in high dimensions
Hiroyuki Takamura, Kyouhei Wakasa
We are interested in almost global existence cases in the general theory for nonlinear wave equations, which are caused by critical exponents of nonlinear terms. Such situations ca…
Almost global solutions of semilinear wave equations with the critical exponent in high dimensions
Hiroyuki Takamura, Kyouhei Wakasa
We are interested in the "almost" global-in-time existence of classical solutions in the general theory for nonlinear wave equations. All the three such cases are known to be sharp…
The blow-up and lifespan of solutions to systems of semilinear wave equation with critical exponents in high dimensions
Yuki Kurokawa, Hiroyuki Takamura, Kyouhei Wakasa
In this paper we prove the blow-up theorem in the critical case for weakly coupled systems of semilinear wave equations in high dimensions. The upper bound of the lifespan of the s…
The sharp upper bound of the lifespan of solutions to critical semilinear wave equations in high dimensions
Hiroyuki Takamura, Kyouhei Wakasa
The final open part of Strauss' conjecture on semilinear wave equations was the blow-up theorem for the critical case in high dimensions. This problem was solved by Yordanov and Zh…