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Global existence to the initial–boundary value problem for a system of nonlinear diffusion and wave equations

Journal of Differential Equations, 2018-01, Vol.264 (1), p.134-162

Nakao, Mitsuhiro

2018

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On the initial-boundary value problem for some quasilinear parabolic equations of divergence form

Journal of Differential Equations, 2017-12, Vol.263 (12), p.8565-8580

Nakao, Mitsuhiro

2017

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Global existence to the initial–boundary value problem for a system of semilinear wave equations

Nonlinear analysis, 2016-11, Vol.146, p.233-257

Nakao, Mitsuhiro

2016

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Computer-assisted proof for the stationary solution existence of the Navier–Stokes equation over 3D domains

Communications in nonlinear science & numerical simulation, 2022-05, Vol.108, p.106223, Article 106223

2022

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On Some Convergence Properties for Finite Element Approximations to the Inverse of Linear Elliptic Operators

Acta cybernetica (Szeged), 2022-09, Vol.26 (1), p.71-82

2022

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Efficient Approaches for Verifying the Existence and Bound of Inverse of Linear Operators in Hilbert Spaces

Journal of scientific computing, 2023-01, Vol.94 (2), p.43, Article 43

2023

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Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations

1st ed. 2019., 2019

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GLOBAL EXISTENCE TO THE INITIAL-BOUNDARY VALUE PROBLEM FOR A SYSTEM OF NONLINEAR DIFFUSION AND WAVE EQUATIONS II

Kyushu Journal of Mathematics, 2018, Vol.72(2), pp.287-306

NAKAO, Mitsuhiro

2018

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Error Constants for the Semi-Discrete Galerkin Approximation of the Linear Heat Equation

Journal of scientific computing, 2021-11, Vol.89 (2), p.34, Article 34

2021

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A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration

Applied mathematics and computation, 2016-03, Vol.276, p.239-251

2016

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Numerical Verification of Solutions for Nonlinear Parabolic Problems

Numerical functional analysis and optimization, 2020-09, Vol.41 (12), p.1495-1514

2020

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A unique continuation property for the wave equation in a time-dependent domain

Journal of mathematical analysis and applications, 2022-01, Vol.505 (1), p.125583, Article 125583

Nakao, Mitsuhiro

2022

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Rigorous numerical inclusion of the blow-up time for the Fujita-type equation

Japan journal of industrial and applied mathematics, 2023-01, Vol.40 (1), p.665-689

2023

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An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space

Japan journal of industrial and applied mathematics, 2019-07, Vol.36 (2), p.407-420

2019

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Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations

Japan journal of industrial and applied mathematics, 2021-06, Vol.38 (2), p.545-559

2021

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A new formulation using the Schur complement for the numerical existence proof of solutions to elliptic problems: without direct estimation for an inverse of the linearized operator

Numerische Mathematik, 2020-12, Vol.146 (4), p.907-926

2020

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Energy decay for a nonlinear generalized Klein-Gordon equation in exterior domains with a nonlinear localized dissipative term

Journal of the Mathematical Society of Japan, 2012, Vol.64 (3), p.851-883

NAKAO, Mitsuhiro

2012

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Constructive error analysis of a full-discrete finite element method for the heat equation

Japan journal of industrial and applied mathematics, 2019-09, Vol.36 (3), p.777-790

2019

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Constructive error estimates for full discrete approximation of periodic solution for heat equation

Journal of computational and applied mathematics, 2020-04, Vol.368, p.112510, Article 112510

2020

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CONSTRUCTIVE A PRIORI ERROR ESTIMATES FOR A FULL DISCRETE APPROXIMATION OF THE HEAT EQUATION

SIAM journal on numerical analysis, 2013-01, Vol.51 (3), p.1525-1541

2013

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An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces

Journal of Differential Equations, 2019-04, Vol.266 (9), p.5431-5447

2019

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VERIFIED COMPUTATIONS OF EIGENVALUE EXCLOSURES FOR EIGENVALUE PROBLEMS IN HILBERT SPACES

SIAM journal on numerical analysis, 2014-01, Vol.52 (2), p.975-992

2014

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On the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems

Numerische Mathematik, 2014-04, Vol.126 (4), p.679-701

2014

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Smoothing effects of the initial-boundary value problem for logarithmic type quasilinear parabolic equations

Journal of mathematical analysis and applications, 2018-06, Vol.462 (2), p.1585-1604

Nakao, Mitsuhiro

2018

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A numerical proof algorithm for the non-existence of solutions to elliptic boundary value problems

Applied numerical mathematics, 2021-11, Vol.169, p.87-107

2021

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Global existence to the initial–boundary value problem for a system of nonlinear diffusion and wave equations

On the initial-boundary value problem for some quasilinear parabolic equations of divergence form

Global existence to the initial–boundary value problem for a system of semilinear wave equations

Computer-assisted proof for the stationary solution existence of the Navier–Stokes equation over 3D domains

On Some Convergence Properties for Finite Element Approximations to the Inverse of Linear Elliptic Operators

Efficient Approaches for Verifying the Existence and Bound of Inverse of Linear Operators in Hilbert Spaces

Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations

GLOBAL EXISTENCE TO THE INITIAL-BOUNDARY VALUE PROBLEM FOR A SYSTEM OF NONLINEAR DIFFUSION AND WAVE EQUATIONS II

Error Constants for the Semi-Discrete Galerkin Approximation of the Linear Heat Equation

A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration

Numerical Verification of Solutions for Nonlinear Parabolic Problems

A unique continuation property for the wave equation in a time-dependent domain

Rigorous numerical inclusion of the blow-up time for the Fujita-type equation

An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space

Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations

A new formulation using the Schur complement for the numerical existence proof of solutions to elliptic problems: without direct estimation for an inverse of the linearized operator

Energy decay for a nonlinear generalized Klein-Gordon equation in exterior domains with a nonlinear localized dissipative term

Constructive error analysis of a full-discrete finite element method for the heat equation

Constructive error estimates for full discrete approximation of periodic solution for heat equation

CONSTRUCTIVE A PRIORI ERROR ESTIMATES FOR A FULL DISCRETE APPROXIMATION OF THE HEAT EQUATION

An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces

VERIFIED COMPUTATIONS OF EIGENVALUE EXCLOSURES FOR EIGENVALUE PROBLEMS IN HILBERT SPACES

On the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems

Smoothing effects of the initial-boundary value problem for logarithmic type quasilinear parabolic equations

A numerical proof algorithm for the non-existence of solutions to elliptic boundary value problems

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