22 citations · 46 across the 11 of their papers we have counts for
12 papers
The global solvability of the Kirchhoff equation with Sobolev data
Tokio Matsuyama, Lenny Neyt
We consider linear and non-linear Cauchy equations in the context of Sobolev spaces. In particular, we show the global existence of solutions to the Kirchhoff equation with initial…
A lower bound for the life span of solutions to the Kirchhoff equation with Gevrey data
Tokio Matsuyama, Lenny Neyt
We provide a new lower bound for the life span of solutions to the Kirchhoff equation for which the initial data belongs to the Gevrey space. This lower bound strictly improves the…
Bilinear estimates in Besov spaces generated by the Dirichlet Laplacian
Tsukasa Iwabuchi, Tokio Matsuyama, Koichi Taniguchi
The purpose of this paper is to establish bilinear estimates in Besov spaces generated by the Dirichlet Laplacian on a domain of Euclidian spaces. These estimates are proved by usi…
On wave equation outside trapping obstacles and local energy decay in odd space dimensions
Vladimir Georgiev, Tokio Matsuyama
The purpose of the present paper is to establish appropriate cut-off resolvent estimates for the Dirichlet Laplacian on exterior domains. The geometrical assumptions on domains are…
Besov spaces on open sets
Tsukasa Iwabuchi, Tokio Matsuyama, Koichi Taniguchi
This paper is devoted to giving definitions of Besov spaces on an arbitrary open set of via the spectral theorem for the Schrödinger operator with the Dirichlet bound…
-mapping properties for Schrödinger operators in open sets of
T. Iwabuchi, T. Matsuyama, K. Taniguchi
Let be a Schrödinger operator on an arbitrary open set of , where , and is the Dirichlet Laplacian and the potential belongs to the Ka…
On the Gevrey well-posedness of the Kirchhoff equation
Tokio Matsuyama, Michael Ruzhansky
This paper is devoted to proving the almost global solvability of the Cauchy problem for the Kirchhoff equation in the Gevrey space . Furthermore, similar results are…
Global well-posedness of the Kirchhoff equation and Kirchhoff systems
Tokio Matsuyama, Michael Ruzhansky
This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data. Similar results…
Global well-posedness of Kirchhoff systems
Tokio Matsuyama, Michael Ruzhansky
The aim of this paper is to establish the global well-posedness for Kirchhoff systems. The new approach to the construction of solutions is based on the asymptotic integratio…
A necessary and sufficient condition on scattering for the regularly hyperbolic systems
Tokio Matsuyama, Michael Ruzhansky
The present paper is devoted to finding a necessary and sufficient condition on the occurence of scattering for the regularly hyperbolic systems with time-dependent coefficients wh…
Asymptotic integration and dispersion for hyperbolic equations
Tokio Matsuyama, Michael Ruzhansky
The aim of this paper is to establish time decay properties and dispersive estimates for strictly hyperbolic equations with homogeneous symbols and with time-dependent coefficients…
Dispersion and asymptotic profiles for Kirchhoff equations
Tokio Matsuyama, Michael Ruzhansky
The aim of this article is to describe asymptotic profiles for the Kirchhoff equation, and to establish time decay properties and dispersive estimates for Kirchhoff equations. For…