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

1st ed. 2019., 2019

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On the physical significance of non-local material parameters in optical metamaterials

New journal of physics, 2023-12, Vol.25 (12), p.123014

2023

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Ground states of a nonlinear curl-curl problem in cylindrically symmetric media

Nonlinear differential equations and applications, 2016-10, Vol.23 (5), Article 52

2016

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Computer-assisted proofs for semilinear elliptic boundary value problems

Japan journal of industrial and applied mathematics, 2009-10, Vol.26 (2-3), p.419-442

Plum, Michael

2009

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Approximate nonradial solutions for the Lane-Emden problem in the ball

Advances in nonlinear analysis, 2022-01, Vol.11 (1), p.268-284

2022

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Operator estimates for homogenization of the Robin Laplacian in a perforated domain

Journal of Differential Equations, 2022-11, Vol.338, p.474-517

2022

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Norm bound computation for inverses of linear operators in Hilbert spaces

Journal of Differential Equations, 2016-04, Vol.260 (7), p.6363-6374

2016

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Eigenvalue Analysis of the Lax Operator for the One-Dimensional Cubic nonlinear Defocusing Schrödinger Equation

SIAM journal on mathematical analysis, 2023-01, Vol.55 (6), p.7399-7425

2023

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Stability of Black Solitons in Optical Systems with Intensity-Dependent Dispersion

SIAM journal on mathematical analysis, 2024-04, Vol.56 (2), p.2521-2568

2024

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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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Eigenvalue excluding for perturbed-periodic one-dimensional Schrödinger operators

Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, 2012-02, Vol.468 (2138), p.545-562

2012

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Breathers and rogue waves for semilinear curl-curl wave equations

Journal of elliptic and parabolic equations, 2023-12, Vol.9 (2), p.757-780

2023

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Dynamics of the black soliton in a regularized nonlinear Schrödinger equation

Proceedings of the American Mathematical Society, 2024-01

2024

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High efficiency laser-assisted H − charge exchange for microsecond duration beams

Physical review. Accelerators and beams, 2017-12, Vol.20 (12), p.120402, Article 120402

2017

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Computer-assisted enclosure methods for elliptic differential equations

Linear algebra and its applications, 2001-02, Vol.324 (1), p.147-187

Plum, Michael

2001

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Computer-assisted Existence Proofs for One-dimensional Schrödinger-Poisson Systems

Acta cybernetica (Szeged), 2020-01, Vol.24 (3), p.373-391

2020

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Homogenization of wire media with a general purpose nonlocal constitutive relation

Journal of the Optical Society of America. B, Optical physics, 2019-08, Vol.36 (8), p.F99

2019

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Inequalities and Applications 2010: Dedicated to the Memory of Wolfgang Walter

1. Aufl., 2012

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Higher order constitutive relations and interface conditions for metamaterials with strong spatial dispersion

Physics letters. A, 2021-10, Vol.412, p.127570, Article 127570

2021

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A Computer-Assisted Uniqueness Proof for a Semilinear Elliptic Boundary Value Problem

Inequalities and Applications 2010, p.31-52

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Orbital Stability of Domain Walls in Coupled Gross--Pitaevskii Systems

SIAM journal on mathematical analysis, 2018-01, Vol.50 (1), p.810-833

2018

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A Breather Construction for a Semilinear Curl-Curl Wave Equation with Radially Symmetric Coefficients

Journal of elliptic and parabolic equations, 2016-04, Vol.2 (1-2), p.371-387

2016

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First Demonstration of Laser-Assisted Charge Exchange for Microsecond Duration H^{-} Beams

Physical review letters, 2017-02, Vol.118 (7), p.074801-074801, Article 074801

2017

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Photonic Crystals: Mathematical Analysis and Numerical Approximation

1. Aufl., 2011

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Error bounds and enclosures: The development of numerical analysis and the impact of the contributions by Lothar Collatz

Zeitschrift für angewandte Mathematik und Mechanik, 2020-10, Vol.100 (10), p.n/a

2020

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

On the physical significance of non-local material parameters in optical metamaterials

Ground states of a nonlinear curl-curl problem in cylindrically symmetric media

Computer-assisted proofs for semilinear elliptic boundary value problems

Approximate nonradial solutions for the Lane-Emden problem in the ball

Operator estimates for homogenization of the Robin Laplacian in a perforated domain

Norm bound computation for inverses of linear operators in Hilbert spaces

Eigenvalue Analysis of the Lax Operator for the One-Dimensional Cubic nonlinear Defocusing Schrödinger Equation

Stability of Black Solitons in Optical Systems with Intensity-Dependent Dispersion

VERIFIED COMPUTATIONS OF EIGENVALUE EXCLOSURES FOR EIGENVALUE PROBLEMS IN HILBERT SPACES

Eigenvalue excluding for perturbed-periodic one-dimensional Schrödinger operators

Breathers and rogue waves for semilinear curl-curl wave equations

Dynamics of the black soliton in a regularized nonlinear Schrödinger equation

High efficiency laser-assisted H − charge exchange for microsecond duration beams

Computer-assisted enclosure methods for elliptic differential equations

Computer-assisted Existence Proofs for One-dimensional Schrödinger-Poisson Systems

Homogenization of wire media with a general purpose nonlocal constitutive relation

Inequalities and Applications 2010: Dedicated to the Memory of Wolfgang Walter

Higher order constitutive relations and interface conditions for metamaterials with strong spatial dispersion

A Computer-Assisted Uniqueness Proof for a Semilinear Elliptic Boundary Value Problem

Orbital Stability of Domain Walls in Coupled Gross--Pitaevskii Systems

A Breather Construction for a Semilinear Curl-Curl Wave Equation with Radially Symmetric Coefficients

First Demonstration of Laser-Assisted Charge Exchange for Microsecond Duration H^{-} Beams

Photonic Crystals: Mathematical Analysis and Numerical Approximation

Error bounds and enclosures: The development of numerical analysis and the impact of the contributions by Lothar Collatz

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