11 citations · 42 across the 16 of their papers we have counts for
16 papers
Computer-assisted proof for the stationary solution existence of the Navier-Stokes equation over 3D domains
Xuefeng Liu, Mitsuhiro T. Nakao, Shin'ichi Oishi
This paper proposes a computer-assisted solution existence verification method for the stationary Navier-Stokes equation over general 3D domains. The proposed method verifies that…
Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations
Xuefeng Liu, Mitsuhiro Nakao, Chun'guang You +1
For the Stokes equation over 2D and 3D domains, explicit a posteriori and a priori error estimation are novelly developed for the finite element solution. The difficulty in handlin…
Numerical verification for asymmetric solutions of the Hénon equation on bounded domains
Taisei Asai, Kazuaki Tanaka, Shin'ichi Oishi
The Hénon equation, a generalized form of the Emden equation, admits symmetry-breaking bifurcation for a certain ratio of the transverse velocity to the radial velocity. Therefore,…
A new formulation for the numerical proof of the existence of solutions to elliptic problems
Kouta Sekine, Mitsuhiro T. Nakao, Shin'ichi Oishi
Infinite-dimensional Newton methods can be effectively used to derive numerical proofs of the existence of solutions to partial differential equations (PDEs). In computer-assisted…
Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems
Kouta Sekine, Kazuaki Tanaka, Shin'ichi Oishi
In numerical existence proofs for solutions of the semi-linear elliptic system, evaluating the norm of the inverse of a perturbed Laplace operator plays an important role. We revea…
Accurate method of verified computing for solutions of semilinear heat equations
Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo +1
We provide an accurate verification method for solutions of heat equations with a superlinear nonlinearity. The verification method numerically proves the existence and local uniqu…
Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains
Makoto Mizuguchi, Kazuaki Tanaka, Kouta Sekine +1
This paper is concerned with an explicit value of the embedding constant from to for a bounded domain , where $1\leq…
Numerical verification method for positiveness of solutions to elliptic equations
Kazuaki Tanaka, Kouta Sekine, Shin'ichi Oishi
In this paper, we propose a numerical method for verifying the positiveness of solutions to semilinear elliptic equations. We provide a sufficient condition for a solution to an el…
Rigorous numerical enclosures for positive solutions of Lane-Emden's equation with sub-square exponents
Kazuaki Tanaka, Michael Plum, Kouta Sekine +2
The purpose of this paper is to obtain rigorous numerical enclosures for solutions of Lane-Emden's equation with homogeneous Dirichlet boundary conditions. We pro…
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…
Sharp numerical inclusion of the best constant for embedding on bounded convex domain
Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi +1
In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding on bounded conv…
Estimation of the Sobolev embedding constant on domains with minimally smooth boundary
Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi +1
In this paper, we propose a method for estimating the Sobolev type embedding constant on a domain with minimally smooth boundary. We estimate the embedding constant by constructing…
Verified computations for hyperbolic 3-manifolds
Neil Hoffman, Kazuhiro Ichihara, Masahide Kashiwagi +3
For a given cusped 3-manifold admitting an ideal triangulation, we describe a method to rigorously prove that either or a filling of admits a complete hyperbolic struct…
Verified eigenvalue evaluation for Laplacian over polygonal domain of arbitrary shape
Xuefeng Liu, Shin'ichi Oishi
The finite element method(FEM) is applied to bound leading eigenvalues of Laplace operator over polygonal domain. Compared with classical numerical methods, most of which can only…
Space guaranteeing a primitive chaotic behavior
Yoshihito Ogasawara, Shin'ichi Oishi
This study describes such a situation that a Cantor set emerges as a result of the exploration of sufficient conditions for the property which is generalized from fundamental chaot…
Estimate of the Hausdorff Dimension of a Self-Similar Set due to Weak Contractions
Yoshihito Ogasawara, Shin'ichi Oishi
As for the remarkable study on the estimate of the Hausdorff dimension of a self-similar set due to weak contractions (Kitada A. et al. Chaos, Solitons & Fractals 13 (2002) 363-366…