52 citations · 416 across the 46 of their papers we have counts for
46 papers
Asymptotic profiles for the Cauchy problem of semilinear beam equation with two variable coefficients in the subcritical case
Mohamed Ali Hamza, Yuta Wakasugi, Shuji Yoshikawa
In this article, we investigate the asymptotic profile of solutions to the Cauchy problem for a nonlinear beam equation with two variable coefficients in the subcritical nonlinear…
Existence of solutions of semilinear wave equations with time-dependent propagation speed and time derivative nonlinearity
Kimitoshi Tsutaya, Yuta Wakasugi
Consider wave equations with time derivative nonlinearity and time-dependent propagation speed which are generalized versions of the wave equations in the Friedmann-Lemaître-Robert…
Existence of solutions to the semilinear damped wave equation with non- slowly decaying data : polynomial nonlinearity case
Masahiro Ikeda, Takahisa Inui, Yuta Wakasugi
We study the Cauchy problem of the semilinear damped wave equation with polynomial nonlinearity, and establish the local and global existence of the solution for slowly decaying in…
Appearance of Strauss-type exponent in semilinear wave equations with time-dependent speed of propagation
Motohiro Sobajima, Kimitoshi Tsutaya, Yuta Wakasugi
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.…
Asymptotic behavior of solutions to elliptic equations in 2D exterior domains
Hideo Kozono, Yutaka Terasawa, Yuta Wakasugi
The asymptotic behavior of solutions to the second order elliptic equations in exterior domains is studied. In particular, under the assumption that the solution belongs to the Lor…
Revisit on global existence of solutions for semilinear damped wave equations in with noncompactly supported initial data
Yuta Wakasugi
In this note, we study the Cauchy problem of the semilinear damped wave equation and our aim is the small data global existence for noncompactly supported initial data. For this pr…
Asymptotic profiles for the Cauchy problem of damped beam equation with two variable coefficients and derivative nonlinearity
Mohamed Ali Hamza, Yuta Wakasugi, Shuji Yoshikawa
In this article we investigate the asymptotic profile of solutions for the Cauchy problem of the nonlinear damped beam equation with two variable coefficients: \[ \partial_t^2 u +…
Lifespan estimates for semilinear damped wave equation in a two-dimensional exterior domain
Masahiro Ikeda, Motohiro Sobajima, Koichi Taniguchi +1
Lifespan estimates for semilinear damped wave equations of the form in a two dimensional exterior domain endowed with the Dirichlet boundary co…
Liouville-type theorems for the new Taylor--Couette flow of the stationary Navier--Stokes equations
Hideo Kozono, Yutaka Terasawa, Yuta Wakasugi
We study the stationary Navier--Stokes equations in the region between two rotating concentric cylinders. We first prove that, under the small Reynolds number, if the fluid is axis…
Asymptotic behavior and Liouville-type theorems for axisymmetric stationary Navier-Stokes equations outside of an infinite cylinder with a periodic boundary condition
Hideo Kozono, Yutaka Terasawa, Yuta Wakasugi
We study the asymptotic behavior of solutions to the steady Navier-Stokes equations outside of an infinite cylinder in . We assume that the flow is periodic in -…
Decay property of solutions to the wave equation with space-dependent damping, absorbing nonlinearity, and polynomially decaying data
Yuta Wakasugi
We study the large time behavior of solutions to the semilinear wave equation with space-dependent damping and absorbing nonlinearity in the whole space or exterior domains. Our re…
Asymptotic expansion of solutions to the wave equation with space-dependent damping
Motohiro Sobajima, Yuta Wakasugi
We study the large time behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We show that if the damping is effective, then the solution i…
Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime
Kimitoshi Tsutaya, Yuta Wakasugi
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…
Global existence and asymptotic behavior for semilinear damped wave equations on measure spaces
Masahiro Ikeda, Koichi Taniguchi, Yuta Wakasugi
This paper is concerned with the semilinear damped wave equation on a measure space with a self-adjoint operator, instead of the standard Laplace operator. Under a certain decay es…
Structure-preserving finite difference schemes for nonlinear wave equations with dynamic boundary conditions
Akihiro Umeda, Yuta Wakasugi, Shuji Yoshikawa
In this article we discuss the numerical analysis for the finite difference scheme of the one-dimensional nonlinear wave equations with dynamic boundary conditions. From the viewpo…
On Glassey's conjecture for semilinear wave equations in Friedmann-Lemaître-Robertson-Walker spacetime
Kimitoshi Tsutaya, Yuta Wakasugi
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 l…
Blow up of solutions of semilinear wave equations in accelerated expanding Friedmann-Lemaître-Robertson-Walker spacetime
Kimitoshi Tsutaya, Yuta Wakasugi
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 accelerat…
On heatlike lifespan of solutions of semilinear wave equations in Friedmann-Lemaître-Robertson-Walker spacetime
Kimitoshi Tsutaya, Yuta Wakasugi
Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat Friedmann-Lemaître-Robertson-Walker spacetimes. We treat the so-called he…
Asymptotic properties of steady solutions to the 3D axisymmetric Navier-Stokes equations with no swirl
Hideo Kozono, Yutaka Terasawa, Yuta Wakasugi
We study the asymptotic behavior of axisymmetric solutions with no swirl to the steady Navier-Stokes equations in the outside of the cylinder. We prove an a priori decay estimate o…
Asymptotic behavior of solutions to elliptic and parabolic equations with unbounded coefficients of the second orderin unbounded domains
Hideo Kozono, Yutaka Terasawa, Yuta Wakasugi
We study an asymptotic behavior of solutions to elliptic equations of the second order in a two dimensional exterior domain. Under the assumption that the solution belongs to …
The Cauchy problem of the semilinear second order evolution equation with fractional Laplacian and damping
Kazumasa Fujiwara, Masahiro Ikeda, Yuta Wakasugi
In the present paper, we prove time decay estimates of solutions in weighted Sobolev spaces to the second order evolution equation with fractional Laplacian and damping for data in…
Supersolutions for parabolic equations with unbounded diffusion and its applications to some classes of parabolic and hyperbolic equations
Motohiro Sobajima, Yuta Wakasugi
This paper is concerned with supersolutions to parabolic equations of the form \begin{equation} \partial_t U (x,t)-D(x)ΔU(x,t)=0, \quad (x,t)\in \mathbb{R}^N \times (0,\infty), \en…
Asymptotic properties of steady and nonsteady solutions to the 2D Navier-Stokes equations with finite generalized Dirichlet integral
Hideo Kozono, Yutaka Terasawa, Yuta Wakasugi
We consider the stationary and non-stationary Navier-Stokes equations in the whole plane and in the exterior domain outside of the large circle. The solution is…
Endpoint Strichartz estimate for the damped wave equation and its application
Takahisa Inui, Yuta Wakasugi
Recently, the Strichartz estimates for the damped wave equation was obtained by the first author except for the wave endpoint case. In the present paper, we give the Strichartz est…