419 citations · 448 across the 27 of their papers we have counts for
28 papers
On Algebraic-Dynamical Correspondence of Oscillatory Blow-Up Solutions for ODEs
Kaname Matsue
We develop an algebraic-dynamical correspondence for type-I oscillatory blow-up solutions of autonomous ODEs with asymptotically quasi-homogeneous vector fields. Periodic solutions…
A Green's Function-Based Enclosure Framework for Poisson's Equation and Generalized Sub- and Super-Solutions
Kazuaki Tanaka, Ryoga Iwanami, Kaname Matsue +1
This paper presents a novel framework for enclosing solutions of Poisson's equation based on generalized sub- and super-solutions constructed using fundamental solutions. The conve…
A simple description of blow-up solutions through dynamics at infinity in nonautonomous ODEs
Kaname Matsue
A simple criterion of the existence of (type-I) blow-up solutions for nonautonomous ODEs is provided. In a previous study [Matsue, SIADS, 24(2025), 415-456], geometric criteria for…
Characterization of Maximizers in A Non-Convex Geometric Optimization Problem With Application to Optical Wireless Power Transfer Systems
Dinh Hoa Nguyen, Kaname Matsue
This research studies a non-convex geometric optimization problem arising from the field of optical wireless power transfer. In the considered optimization problem, the cost functi…
Blow-up behavior for ODEs with normally hyperbolic nature in dynamics at infinity
Kaname Matsue
We describe blow-up behavior for ODEs by means of dynamics at infinity with complex asymptotic behavior in autonomous systems, as well as in nonautonomous systems. Based on precedi…
Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. II -- Dynamical Correspondence
Hisatoshi Kodani, Kaname Matsue, Hiroyuki Ochiai +1
In this paper, we provide a natural correspondence of eigenstructures of Jacobian matrices associated with equilibria for appropriately transformed two systems describing finite-ti…
Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. I -- Method and Justification
Taisei Asai, Hisatoshi Kodani, Kaname Matsue +2
In this paper, we provide a systematic methodology for calculating multi-order asymptotic expansion of blow-up solutions near blow-up for autonomous ordinary differential equations…
A mathematical treatment of bump structure for the particle laden flows with particle features
Kaname Matsue, Kyoko Tomoeda
In this paper, we consider the particle laden flows on a inclined plane under the effect of the gravity. It is observed from preceding experimental works that the particle-rich rid…
Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs: Validation and Extraction of Global Nature
Jean-Philippe Lessard, Kaname Matsue, Akitoshi Takayasu
In this paper, blow-up solutions of autonomous ordinary differential equations (ODEs) which are unstable under perturbations of initial points, referred to as saddle-type blow-up s…
A refined asymptotic behavior of traveling wave solutions for degenerate nonlinear parabolic equations
Yu Ichida, Kaname Matsue, Takashi Okuda Sakamoto
In this paper, we consider the asymptotic behavior of traveling wave solutions of the degenerate nonlinear parabolic equation: ( or ) for $ξ\equ…
A crossover between open quantum random walks to quantum walks
Norio Konno, Kaname Matsue, Etsuo Segawa
We propose an intermediate walk continuously connecting an open quantum random walk and a quantum walk with parameters controlling a decoherence effect; if ,…
Rigorous numerics of blow-up solutions for ODEs with exponential nonlinearity
Kaname Matsue, Akitoshi Takayasu
Our concerns here are blow-up solutions for ODEs with exponential nonlinearity from the viewpoint of dynamical systems and their numerical validations. As an example, the finite di…
Geometric treatments and a common mechanism in finite-time singularities for autonomous ODEs
Kaname Matsue
Geometric treatments of blow-up solutions for autonomous ordinary differential equations and their blow-up rates are concerned. Our approach focuses on the type of invariant sets a…
Rigorous numerics of finite-time singularities in dynamical systems - methodology and applications
Kaname Matsue
This paper aims at providing rigorous numerical computation procedure for finite-time singularities in dynamical systems. Combination of time-scale desingularization as well as Lya…
Toward a mathematical analysis for a model of suspension flowing down an inclined plane
Kaname Matsue, Kyoko Tomoeda
We consider the Riemann problem of the dilute approximation equations with spatiotemporally dependent volume fractions from the full model of suspension, in which the particles set…
Resonant-tunneling in discrete-time quantum walk
Kaname Matsue, Leo Matsuoka, Osamu Ogurisu +1
We show that discrete-time quantum walks on the line, , behave as "the quantum tunneling". In particular, quantum walkers can tunnel through a double-well with the tran…
Numerical validation of blow-up solutions with quasi-homogeneous compactifications
Kaname Matsue, Akitoshi Takayasu
We provide a numerical validation method of blow-up solutions for finite dimensional vector fields admitting asymptotic quasi-homogeneity at infinity. Our methodology is based on q…
Quantum Search on Simplicial Complexes
Kaname Matsue, Osamu Ogurisu, Etsuo Segawa
In this paper, we propose an extension of quantum searches on graphs driven by quantum walks to simplicial complexes. To this end, we newly define a quantum walk on simplicial comp…
Quaternionic quantum walks of Szegedy type and zeta functions of graphs
Norio Konno, Kaname Matsue, Hideo Mitsuhashi +1
We define a quaternionic extension of the Szegedy walk on a graph and study its right spectral properties. The condition for the transition matrix of the quaternionic Szegedy walk…
Rigorous numerics of tubular, conic, star-shaped neighborhoods of slow manifolds for fast-slow systems
Kaname Matsue
We provide a rigorous numerical computation method to validate tubular neighborhoods of normally hyperbolic slow manifolds with the explicit radii for the fast-slow system \begin{e…
On blow-up solutions of differential equations with Poincaré-type compactifications
Kaname Matsue
We provide explicit criteria for blow-up solutions of autonomous ordinary differential equations. Ideas are based on the quasi-homogeneous desingularization (blowing-up) of singula…
Numerical validation of blow-up solutions of ordinary differential equations
Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki +3
This paper focuses on blow-up solutions of ordinary differential equations (ODEs). We present a method for validating blow-up solutions and their blow-up times, which is based on c…
On the construction of Lyapunov functions with computer assistance
Kaname Matsue, Tomohiro Hiwaki, Nobito Yamamoto
Computer assisted procedures of Lyapunov functions defined in given neighborhoods of fixed points for flows and maps are discussed. We provide a systematic methodology for construc…
A note on the spectral mapping theorem of quantum walk models
Kaname Matsue, Osamu Ogurisu, Etsuo Segawa
We discuss the description of eigenspace of a quantum walk model with an associating linear operator in abstract settings of quantum walk including the Szegedy walk on grap…