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OpenAlex Citation Counts

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OpenAlex is a bibliographic catalogue of scientific papers, authors and institutions accessible in open access mode, named after the Library of Alexandria. It's citation coverage is excellent and I hope you will find utility in this listing of citing articles!

If you click the article title, you'll navigate to the article, as listed in CrossRef. If you click the Open Access links, you'll navigate to the "best Open Access location". Clicking the citation count will open this listing for that article. Lastly at the bottom of the page, you'll find basic pagination options.

Requested Article:

Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq Equation
Roberto Castelli, Marcio Gameiro, J. Lessard
Archive for Rational Mechanics and Analysis (2017) Vol. 228, Iss. 1, pp. 129-157
Open Access | Times Cited: 33

Showing 1-25 of 33 citing articles:

Computer-assisted proofs in PDE: a survey
Javier Gómez-Serrano
SeMA Journal (2019) Vol. 76, Iss. 3, pp. 459-484
Open Access | Times Cited: 56
Automatic differentiation for Fourier series and the radii polynomial approach
Jean‐Philippe Lessard, J. D. Mireles James, Julian Ransford
Physica D Nonlinear Phenomena (2016) Vol. 334, pp. 174-186
Open Access | Times Cited: 40
Validated integration of semilinear parabolic PDEs
Jan Bouwe van den Berg, Maxime Breden, Ray Sheombarsing
Numerische Mathematik (2024) Vol. 156, Iss. 4, pp. 1219-1287
Closed Access | Times Cited: 3
Validation of the bifurcation diagram in the 2D Ohta–Kawasaki problem
Jan Bouwe van den Berg, Jim Williams
Nonlinearity (2017) Vol. 30, Iss. 4, pp. 1584-1638
Open Access | Times Cited: 36
Asymptotically self-similar blowup of the Hou-Luo model for the 3D Euler equations
Jiajie Chen, Thomas Y. Hou, De Huang
Annals of PDE (2022) Vol. 8, Iss. 2
Closed Access | Times Cited: 14
Unstable Stokes Waves
Vera Mikyoung Hur, Zhao Yang
Archive for Rational Mechanics and Analysis (2023) Vol. 247, Iss. 4
Open Access | Times Cited: 8
An A Posteriori KAM Theorem for Whiskered Tori in Hamiltonian Partial Differential Equations with Applications to some Ill-Posed Equations
Rafael de la Llave, Yannick Sire
Archive for Rational Mechanics and Analysis (2018) Vol. 231, Iss. 2, pp. 971-1044
Closed Access | Times Cited: 25
Rigorously Computing Symmetric Stationary States of the Ohta--Kawasaki Problem in Three Dimensions
Jan Bouwe van den Berg, Jim Williams
SIAM Journal on Mathematical Analysis (2019) Vol. 51, Iss. 1, pp. 131-158
Open Access | Times Cited: 22
Computer Assisted Fourier Analysis in Sequence Spaces of Varying Regularity
Jean‐Philippe Lessard, J. D. Mireles James
SIAM Journal on Mathematical Analysis (2017) Vol. 49, Iss. 1, pp. 530-561
Closed Access | Times Cited: 23
Fourier–Taylor parameterization of unstable manifolds for parabolic partial differential equations: Formalism, implementation and rigorous validation
Christian Reinhardt, J. D. Mireles James
Indagationes Mathematicae (2018) Vol. 30, Iss. 1, pp. 39-80
Open Access | Times Cited: 22
A General Method for Computer-Assisted Proofs of Periodic Solutions in Delay Differential Problems
Jan Bouwe van den Berg, C. M. Groothedde, Jean‐Philippe Lessard
Journal of Dynamics and Differential Equations (2020) Vol. 34, Iss. 2, pp. 853-896
Closed Access | Times Cited: 20
Spontaneous Periodic Orbits in the Navier–Stokes Flow
Jan Bouwe van den Berg, Maxime Breden, J. LESSARD, et al.
Journal of Nonlinear Science (2021) Vol. 31, Iss. 2
Closed Access | Times Cited: 17
Global dynamics in nonconservative nonlinear Schrödinger equations
Jonathan Jaquette, Jean‐Philippe Lessard, Akitoshi Takayasu
Advances in Mathematics (2022) Vol. 398, pp. 108234-108234
Open Access | Times Cited: 11
Improved growth estimate for one-dimensional sixth-order Boussinesq equation with logarithmic nonlinearity
Zhuang Han, Runzhang Xu
Applied Mathematics Letters (2024) Vol. 160, pp. 109290-109290
Closed Access | Times Cited: 1
Families of Periodic Solutions for Some Hamiltonian PDEs
Gianni Arioli, Hans Koch
SIAM Journal on Applied Dynamical Systems (2017) Vol. 16, Iss. 1, pp. 1-15
Open Access | Times Cited: 14
Computer-Assisted Proof of Heteroclinic Connections in the One-Dimensional Ohta--Kawasaki Model
Jacek Cyranka, Thomas Wanner
SIAM Journal on Applied Dynamical Systems (2018) Vol. 17, Iss. 1, pp. 694-731
Open Access | Times Cited: 14
Stable manifolds to bounded solutions in possibly ill-posed PDEs
Hongyu Cheng, Rafael de la Llave
Journal of Differential Equations (2019) Vol. 268, Iss. 8, pp. 4830-4899
Open Access | Times Cited: 11
Spontaneous periodic orbits in the Navier-Stokes flow
Jan Bouwe van den Berg, Maxime Breden, Jean‐Philippe Lessard, et al.
(2019)
Closed Access | Times Cited: 7
Convexity of Whitham's highest cusped wave
Alberto Enciso, Javier Gómez-Serrano, Bruno Vergara
arXiv (Cornell University) (2018)
Open Access | Times Cited: 6
Validated Spectral Stability via Conjugate Points
Margaret Beck, Jonathan Jaquette
SIAM Journal on Applied Dynamical Systems (2022) Vol. 21, Iss. 1, pp. 366-404
Open Access | Times Cited: 4
Persistence of Periodic Orbits under State-dependent Delayed Perturbations: Computer-assisted Proofs
Joan Gimeno, Jean‐Philippe Lessard, J. D. Mireles James, et al.
SIAM Journal on Applied Dynamical Systems (2023) Vol. 22, Iss. 3, pp. 1743-1779
Open Access | Times Cited: 2
Some unexpected results on the Brillouin singular equation: Fold bifurcation of periodic solutions
Roberto Castelli, Maurizio Garrione
Journal of Differential Equations (2018) Vol. 265, Iss. 6, pp. 2502-2543
Open Access | Times Cited: 4
Parameterized stable/unstable manifolds for periodic solutions of implicitly defined dynamical systems
Archana Timsina, J. D. Mireles James
Chaos Solitons & Fractals (2022) Vol. 161, pp. 112345-112345
Open Access | Times Cited: 3
Periodic and Quasiperiodic Waves on the Sphere
Gianni Arioli, Hans P. Koch
SIAM Journal on Applied Dynamical Systems (2024) Vol. 23, Iss. 4, pp. 2769-2792
Closed Access
Dynamical behavior of the long waves on the surface of the water with a small amplitude in none–dimensional nonlinear lattices
Hongwei Ma, Fuzhang Wang, Mostafa M. A. Khater, et al.
Journal of Ocean Engineering and Science (2022)
Open Access | Times Cited: 2
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