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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:

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

Showing 1-25 of 56 citing articles:

A Rigorous Integrator and Global Existence for Higher-Dimensional Semilinear Parabolic PDEs via Semigroup Theory
Gabriel William Duchesne, Jean‐Philippe Lessard, Akitoshi Takayasu
Journal of Scientific Computing (2025) Vol. 102, Iss. 3
Open Access
Determination of Stable Branches of Relative Equilibria of the N-Vortex Problem on the Sphere
Kevin Constantineau, Carlos García-Azpeitia, Luis C. García-Naranjo, et al.
Communications in Mathematical Physics (2025) Vol. 406, Iss. 2
Open Access
Smooth imploding solutions for 3D compressible fluids
Tristan Buckmaster, Gonzalo Cao Labora, Javier Gómez-Serrano
Forum of Mathematics Pi (2025) Vol. 13
Open Access
Constructive proofs of existence and stability of solitary waves in the Whitham and capillary–gravity Whitham equations
Matthieu Cadiot
Nonlinearity (2025) Vol. 38, Iss. 3, pp. 035021-035021
Open Access
Computer assisted existence proofs for parameterized cycle-to-cycle connections
J. D. Mireles James, Maxime Murray
Journal of Computational Dynamics (2025)
Open Access
Branches and bifurcations of ejection–collision orbits in the planar circular restricted three body problem
Gianni Arioli, J. D. Mireles James
Nonlinearity (2025) Vol. 38, Iss. 4, pp. 045010-045010
Open Access
Highest cusped waves for the fractional KdV equations
Joel Dahné
Journal of Differential Equations (2024) Vol. 401, pp. 550-670
Open Access | Times Cited: 3
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
Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems
Maxime Breden, Maximilian Engel
The Annals of Applied Probability (2023) Vol. 33, Iss. 2
Open Access | Times Cited: 9
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
On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equations
Jiajie Chen, Thomas Y. Hou, De Huang
Communications on Pure and Applied Mathematics (2021) Vol. 74, Iss. 6, pp. 1282-1350
Open Access | Times Cited: 18
Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem
Maciej J. Capiński, Shane Kepley, J. D. Mireles James
Journal of Differential Equations (2023) Vol. 366, pp. 132-191
Open Access | Times Cited: 7
Stationary non-radial localized patterns in the planar Swift-Hohenberg PDE: Constructive proofs of existence
Matthieu Cadiot, Jean‐Philippe Lessard, Jean‐Christophe Nave
Journal of Differential Equations (2024) Vol. 414, pp. 555-608
Open Access | Times Cited: 2
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
A Posteriori Validation of Generalized Polynomial Chaos Expansions
Maxime Breden
SIAM Journal on Applied Dynamical Systems (2023) Vol. 22, Iss. 2, pp. 765-801
Open Access | Times Cited: 5
Constructive proofs for localised radial solutions of semilinear elliptic systems on Rd
Jan Bouwe van den Berg, Olivier Hénot, Jean‐Philippe Lessard
Nonlinearity (2023) Vol. 36, Iss. 12, pp. 6476-6512
Open Access | Times Cited: 5
Validated Numerical Approximation of Stable Manifolds for Parabolic Partial Differential Equations
Jan Bouwe van den Berg, Jonathan Jaquette, J. D. Mireles James
Journal of Dynamics and Differential Equations (2022) Vol. 35, Iss. 4, pp. 3589-3649
Closed Access | Times Cited: 8
Rigorous Computation of Solutions of Semilinear PDEs on Unbounded Domains via Spectral Methods
Matthieu Cadiot, J. LESSARD, Jean‐Christophe Nave
SIAM Journal on Applied Dynamical Systems (2024) Vol. 23, Iss. 3, pp. 1966-2017
Open Access | Times Cited: 1
Computer assisted proofs of two-dimensional attracting invariant tori for ODEs
Maciej J. Capiński, Emmanuel Fleurantin, J. D. Mireles James
Discrete and Continuous Dynamical Systems (2020) Vol. 40, Iss. 12, pp. 6681-6707
Open Access | Times Cited: 9
Parameterization of Unstable Manifolds for DDEs: Formal Series Solutions and Validated Error Bounds
Olivier Hénot, Jean‐Philippe Lessard, J. D. Mireles James
Journal of Dynamics and Differential Equations (2021) Vol. 34, Iss. 2, pp. 1285-1324
Closed Access | Times Cited: 7
Rigorous verification of Hopf bifurcations in functional differential equations of mixed type
Kevin E. M. Church, Jean‐Philippe Lessard
Physica D Nonlinear Phenomena (2021) Vol. 429, pp. 133072-133072
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
Optimal periodic structures with general space group symmetries in the Ohta–Kawasaki problem
Jan Bouwe van den Berg, Jim Williams
Physica D Nonlinear Phenomena (2020) Vol. 415, pp. 132732-132732
Open Access | Times Cited: 6
Computer-assisted proofs for some nonlinear diffusion problems
Maxime Breden
Communications in Nonlinear Science and Numerical Simulation (2022) Vol. 109, pp. 106292-106292
Open Access | Times Cited: 4
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