419 citations · 448 across the 27 of their papers we have counts for
9 papers · 1 filter
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 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…
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…
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…
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 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…
Rigorous numerics for fast-slow systems with one-dimensional slow variable: topological shadowing approach
Kaname Matsue
We provide a rigorous numerical computation method to validate periodic, homoclinic and heteroclinic orbits as the continuation of singular limit orbits for the fast-slow system $x…