14 citations · 107 across the 28 of their papers we have counts for
6 papers · 2 filters
Asymptotic behavior for the long-range nonlinear Schrödinger equation on star graph with the Kirchhoff boundary condition
Kazuki Aoki, Takahisa Inui, Hayato Miyazaki +2
We consider the cubic nonlinear Schrödinger equation on the star graph with the Kirchhoff boundary condition. We prove modified scattering for the final state problem and the initi…
Scattering theory in homogeneous Sobolev spaces for Schrödinger and wave equations with rough potentials
Haruya Mizutani
We study the scattering theory for the Schrödinger and wave equations with rough potentials in a scale of homogeneous Sobolev spaces. The first half of the paper concerns with an i…
Remarks on asymptotic order for the linear wave equation with the scale-invariant damping and mass with -data
Takahisa Inui, Haruya Mizutani
In the present paper, we consider the linear wave equation with the scale-invariant damping and mass. It is known that the global behavior of the solution depends on the size of th…
Scattering and asymptotic order for the wave equations with the scale-invariant damping and mass
Takahisa Inui, Haruya Mizutani
We consider the linear wave equation with the time-dependent scale-invariant damping and mass. We also treat the corresponding equation with the energy critical nonlinearity. Our a…
Global Kato smoothing and Strichartz estimates for higher-order Schrödinger operators with rough decay potentials
Haruya Mizutani, Xiaohua Yao
Let \( H = (-Δ)^m + V \) be a higher-order elliptic operator on \( L^2(\mathbb{R}^n) \), where \( V \) is a general bounded decaying potential. This paper focuses on the global Kat…
Kato smoothing, Strichartz and uniform Sobolev estimates for fractional operators with sharp Hardy potentials
Haruya Mizutani, Xiaohua Yao
Let and be Schrödinger type operators on with a class of scaling-critical potentials , which include the Hardy potential …