UMONS
Faculty of ScienceDepartment of MathematicsNumerical Analysis TeamRecherche
Research Interests
The team investigates the qualitative properties of non-linear partial differential equations as well as their numerical investigation through numerical simulations. In particular, we are interested in
- existence and multiplicity of solutions, especially when the equations possess a variational formulation;
- symmetry and monotonicity of solutions;
- mountain pass and modified mountain pass algorithms;
- computer assisted proofs.
Publications
2020
Congress proceedings with peer-reviewing
- , Influence of the Choice of the Parameters on Constitutive Models and their Effects on the Results of Ti6Al4V Orthogonal Cutting Simulation, Esaform 2020, Cottbus, Allemagne, 2020.
Popularization
- , Quand les extrêmes sont les meilleurs !, 2020, Institut Saint André, 7520 Ramegnies Chin.
2019
Referenced Publications
- , A non-variational system involving the critical Sobolev exponent. The radial case., Journal d'Analyse Mathématique, (2019), Magnes Press. arXiv: 1603.05641.
- , Comparison of Johnson-Cook and modified Johnson-Cook material constitutive models and their influence on finite element modelling of Ti6Al4V orthogonal cutting process, AIP Conference Proceedings, 2113 (2019), American Institute of Physics. DOI: 10.1063/1.5112617.
Popularization
- , Optimisation — Quand les extrêmes sont les meilleurs !, 2019, Collège Saint Guibert, Gembloux.
Presentations & posters with abstract
- , A computer assisted proof of the symmetries of least energy nodal solutions on squares, Second Days Of Nonlinear Elliptic PDE in Hauts-de-France, Calais, France, 2019.
2018
Referenced Publications
- , Entire radial and nonradial solutions for systems with critical growth, Calculus of Variations and Partial Differential Equations, 57 (2018), Springer. arXiv: 1612.03510.
Popularization
- , Optimisation — Quand les extrêmes sont les meilleurs !, 2018, École des Ursulines, Mons.
- , Optimisation — Quand les extrêmes sont les meilleurs !, 2018, École IPET, Nivelles rue du Paradis 79A - 1400 NIVELLES.
Presentations & posters with abstract
- , Une preuve assistée par ordinateur pour les symétries des solutions nodales d'énergie minimale de Lane-Emden sur le carré, Séminaire d’analyse appliquée A³, Amiens, France, 2018.
Presentations & posters without abstract
- , Le numérique au service de l'apprentissage. Exemples de pratiques enseignantes, Educode, Bruxelles, Belgique, 2018.
- , Superstable expansions of (Z,+,0), Logic Colloquium 2018, Udine, Italie, 2018.
2017
Referenced Publications
- , Spectral analysis of a generalized buckling problem on a ball, Positivity, 21 (2017), pp. 1319–1340, Birkhäuser. DOI: 10.1007/s11117-017-0469-x, arXiv: 1610.04840.
Popularization
- , Optimisation — Quand les extrêmes sont les meilleurs !, 2017, Collège St Benoit, Maredsous.
- , Optimisation — Quand les extrêmes sont les meilleurs !, 2017, Collège Notre-Dame de Tournai, Tournai.
- , Les procédures de vote sous la loupe mathématique, 2017, Collège Notre-Dame de Tournai, Tournai.
- , Les procédures de vote sous la loupe mathématique, 2017, École Vallée Bailly, Braine-l'Alleud.
Presentations & posters with abstract
- , A computer assisted proof of the symmetry of solutions to a PDE, Computers in Scientific Discovery 8, Mons, Belgium, 2017.
- , Radial and non-radial positive solutions to a system with critical growth on ℝᴺ, First days of Nonlinear Elliptic PDE in Hauts-de-France, Valenciennes, France, 2017.
2016
Referenced Publications
- , Multiple radial positive solutions of semilinear elliptic problems with Neumann boundary conditions, Nonlinear Analysis: Theory, Methods and Applications, (2016), pp. 236–273, Elsevier. arXiv: 1603.05610, DOI: 10.1016/j.na.2016.09.010.
Popularization
- , Les procédures de vote sous la loupe mathématique, 2016, Athénée Royal de Nivelles, Nivelles.
- , Quand les extrêmes sont les meilleurs !, 2016, Collège Saint Benoit, Maredsous.
Presentations & posters without abstract
- , Superstable expasions of (Z,+,0), Second Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies, Logroño, Espagne, 2016.
- , Expansions superstables du groupe des entiers, Séminaire des jeunes chercheurs de l'UMONS, Mons, Belgique, 2016.
2015
Referenced Publications
- , Asymptotic symmetries for fractional operators, Nonlinear Analysis: Real World Applications, 26 (2015), pp. 351–371, Elsevier. arXiv: 1407.4029, DOI: 10.1016/j.nonrwa.2015.06.001.
- , Nodal properties of eigenfunctions of a generalized buckling problem on balls, Positivity, (2015), Birkhäuser. arXiv: 1408.6180, DOI: 10.1007/s11117-015-0331-y.
Presentations & posters with abstract
- , On positive solutions to the Lane-Emden problem with Neumann boundary conditions, Séminaire ANEDP - Analyse non linéaire et EDP, Bruxelles, Belgique, 2015.
- , Tools to explore the OPAM Community, OCaml 2015, Vancouver, Canada, 2015.
- , Nodal properties of eigenfunctions of a generalized buckling problem on balls, 8ème édition de la Matinée des Chercheurs 2015 (MdC2015), Mons, Belgique, 2015.
2014
Referenced Publications
- , Convergence of a mountain pass type algorithm for strongly indefinite problems and systems, Electronic Journal of Differential Equations, Conference 21 (2014), pp. 129–147, Texas State University - San Marcos. arXiv: 1301.1456.
Popularization
- , Optimisation: quand les extrêmes sont les meilleurs, 2014, JMS, UMONS.
- , Optimisation: quand les extrêmes sont les meilleurs, 2014, JMS, UMONS.
- , Optimisation — quand les extrêmes sont les meilleurs, 2014, Institut Sainte-Marie, La Louvière.
Presentations & posters with abstract
- , Biocaml: The OCaml Bioinformatics Library, Bioinformatics Open Source Conference (BOSC 2014), Boston, US-MA, 2014.
- , Solutions positives de l'équation de Lane-Emden avec conditions au bord de Neumann, Séminaire du LAMAV, Valenciennes, France, 2014.
2013
Referenced Publications
- , On the Mountain-pass algorithm for the quasi-linear Schrodinger equation, Discrete and Continuous Dynamical Systems, 18 (2013), pp. 1345–1360, Dept. of Mathematics, Southwest Missouri State University. arXiv: 1205.0517, DOI: 10.3934/dcdsb.2013.18.1345.
- , Lane Emden problems with large exponents and singular Liouville equations, Journal de Mathématiques Pures et Appliquées, (2013), Elsevier.
- , Nonlinear Schrödinger problems: symmetries of some variational solutions, NoDEA. Nonlinear Differential Equations and Applications, 20 (2013), pp. 511–521, Birkhauser Verlag. DOI: 10.1007/s00030-012-0163-4.
- , Lane-Emden problems: Asymptotic behavior of low energy nodal solutions, Annales de L'Institut Henri Poincaré. Analyse Non Linéaire, 30 (2013), pp. 121–140, Elsevier. DOI: 10.1016/j.anihpc.2012.06.005.
Publications (not referenced)
- , Mathematical study of wrinkling shapes of thin membranes, 2013.
- , oasis2opam, software, 2013.
Popularization
- , Les dérivées dans le monde du sport, 2013, Institut Saint-Laurent, Marche-en-Famenne.
- , Maths en rue: Quiz Mathématique, 2013, Math en Rue, Bruxelles.
- , Optimisation — quand les extrêmes sont les meilleurs, 2013, Athénée Royal Vauban, Charleroi.
- , La théorie des graphes au secours des géographes, 2013, Printemps des Sciences, UMONS.
- , Optimisation — quand les extrêmes sont les meilleurs, 2013, Centre Scolaire Ma Campagne, Ixelles.
- , Les dérivées dans le monde du sport, 2013, invitation Ecole secondaire, Athenée de Nivelles.
Presentations & posters with abstract
- , Multiplicity and symmetry of positive solutions to semi-linear elliptic problems with Neumann boundary conditions, International Workshop on Variational Problems and PDE's, São Paulo, Brazil, 2013.
- , Multiplicité et symétrie des solutions positives de problèmes semilinéaires elliptiques avec conditions au bord de Neumann, Séminaire A³, Amiens, France, 2013.
- , Convergence of MPA for indefinite problems, systems and quasi-linear problems, P(n)-seminar, Rome, Italy, 2013.
2012
Referenced Publications
- , A mountain pass algorithm with projector, Journal of Computational and Applied Mathematics, 236 (2012), pp. 2025–2036, Elsevier. DOI: 10.1016/j.cam.2011.11.011.
Publications (not referenced)
- , Delimited Overloading, software, 2012.
- , Archimedes: a scientific 2D plotting library, software, 2012.
- , Mesh: a collection of algorithms to build and manipulate triangular meshes, software, 2012.
- , Identification des peptides au moyen des modèles de Markov cachés, Master thesis, 2012, UMONS.
- , L-BFGS: a binding to the code by J. Nocedal giving a quasi-Newton method for the optimization of functions of many variables, software, 2012.
- , Odepack: an OCaml interface to the celebrated collection of code to numerically solve systems of ordinary differential equations, software, 2012.
Popularization
- , Optimisation — quand les extrêmes sont les meilleurs, 2012, Institut Saint-Laurent, Marche-en-Famenne.
- , Quiz Mathématique, 2012, Printemps des Sciences, UMONS, Mons.
Presentations & posters with abstract
- , Multiplicity and symmetry of positive solutions to semi-linear elliptic problems with Neumann boundary conditions, Variational and Topological problems, Flagstaff, USA, 2012.
- , Lane-Emden problems: Asymptotic behavior of low energy nodal solutions, Variational and Topological problems, Flagstaff, USA, 2012.
- , Wrinkling of thin membranes laying on fluid substrates under small compression, Spring School in Nonlinear Partial Differential Equations, Brussels, Belgium, 2012.
- , Lane-Emden problems: Asymptotic behavior of low energy nodal solutions, Spring School in Nonlinear Partial Differential Equations, Brussels, Belgium, 2012.
Presentations & posters without abstract
- , One-dimensional wrinkling of thin films, Frontiers of Mathematics and Applications III, Santander, Espagne, 2012.
- , Lane-Emden problems: Asymptotic behavior of low energy nodal solutions, groupe de contact FNRS (EDP et semi-groupe), Louvain-la-Neuve, Belgium, 2012.
- , Nonlinear Schrödinger problems: existence, symmetry and numerical approaches, Séminaire du Laboratoire Paul Painlevé, Lille, France, 2012.
- , Symmetry and symmetry breaking of least energy (nodal) solutions of semi-linear elliptic problems with Neumann boundary conditions, Séminaire, Université Toulouse 1 — Capitole, France, 2012.
2011
Publications (not referenced)
- , OCaml CSV, software, 2011.
- , L'ordinateur au cœur de la découverte mathématique, Élement: le Magazine de l'Université de Mons, 5 (2011), pp. 29–31, Université de Mons.
Popularization
- , Les procédures de vote sous la loupe mathématique, 2011, Institut Saint-Laurent, Marche-en-Famenne.
- , Optimisation — quand les extrêmes sont les meilleurs, 2011, École Jean Rey, Couvin.
- , Quiz Mathématique, 2011, Printemps des Sciences, UMONS, Mons.
- , Les mathématiques dans le monde du sport, 2011, Journée Math/Sciences, UMONS, Mons.
- , Atelier de robotique : Rubik's cube & Puissance 4, 2011, Printemps des Sciences, UMONS, Mons.
Presentations & posters with abstract
- , Nonlinear Schrödinger problems : survey about existence, symmetry and multiplicity results, EU-Young workshop in mathematics, Grenade, Espagne, 2011.
Presentations & posters without abstract
- , One-dimensional wrinkling of thin films, Higher order equations in Geometry and Physics, Trieste, Italie, 2011.
- , Schrödinger problems with Neumann boundary conditions, séminaire LAMAV, Valenciennes, France, 2011.
- , Nonlinear PDEs : multiplicity, numerical approaches and symmetries, 6ème édition de la Matinée des Chercheurs (MDC 2011), Mons, Belgique, 2011.
- , One-dimensional wrinkling of thin films, Matinée des Chercheurs 2011, Université de Mons, Belgique, 2011.
- , Nonlinear Schrödinger problems : multiplicity and symmetry of positive solutions, Nonlinear PDE and harmonic analysis, Rome, Italie, 2011.
2010
Referenced Publications
- , Oddness of least energy nodal solutions on radial domains, Electronic Journal of Differential Equations, Conference 18 (2010), pp. 23–31, Texas State University - San Marcos. ISSN: 1072-6691.
Publications (not referenced)
- , Symmetries of solutions for nonlinear Schrödinger equations : numerical and theoretical approaches, 2010.
Popularization
- , Mathematical education in Belgium, 2010, invitation de l'Université du Connecticut, UCONN, Storrs (USA).
- , Atelier de robotique : Puissance 4, 2010, Printemps des Sciences, UMONS, Mons.
Presentations & posters with abstract
- , Wrinkling of thin membranes on fluid substrates., Workshop on Variational Methods in Nonlinear Differential Equations, Oaxaca, Mexique, 2010.
- , Nonlinear Schrödinger problems : survey about symmetries, PhD Day (BMS), Bruxelles, Belgique, 2010.
Presentations & posters without abstract
- , Lane Emden problem : survey about symmetries, PDE and Image Analysis seminar, Storrs, USA, 2010.
- , One-dimensional wrinkling of thin membranes, PhD Day (BMS), Bruxelles, Belgique, 2010.
- , One-dimensional wrinkling of thin membranes, Workshop on thin structures, Naples, Italie, 2010.
- , Nonlinear Schrödinger problems : Mountain Pass algorithms, PDE and Image Analysis seminar, Storrs, USA, 2010.
- , Oddness of least energy nodal solutions of the Lane-Emden problem., Johann Wolfgang Goethe-Universität, Frankfurt, Allemagne, 2010.
2009
Referenced Publications
- , Asymptotics and symmetries of ground state and least energy nodal solutions for boundary value problems with slowly growing superlinearities, Differential and Integral Equations, 22 (2009), pp. 1047–1074, Khayyam Publishing.
- , Nodal line structure of least energy nodal solutions for Lane-Emden problems, Comptes Rendus. Mathématique, 347 (2009), pp. 767–771, Elsevier Masson. DOI: 10.1016/j.crma.2009.04.023.
Publications (not referenced)
- , Lego Mindstorm library, software, 2009.
- , Stabilité, Bifurcations et Classification des Elastica, Master thesis, 2009, UMONS.
Popularization
- , Atelier de robotique : Labyrinthe & Rubik's cube, 2009, La fête des Maths et des Jeux dans le cadre de la fête de la Science, Lille.
- , Atelier de robotique : Labyrinthe & Rubik's cube, 2009, Printemps des Sciences, UMONS, Mons.
- , Atelier de robotique, 2009, Congrès des sciences, Mons.
- , Pourquoi Rafael Nadal gagne-t-il si souvent Roland Garros?, 2009, Invitation de D.Nicolay, Athenée Vauban, Charleroi.
- , Les dérivées dans le monde du sport, 2009, Journée des sciences, UMH, Mons.
- , Dérivées et sport, 2009, invitation Ecole secondaire, Athenée Marguerite Bervoets, Mons.
Presentations & posters with abstract
- , Symmetries of ground state solutions for Neumann Lane-Emden problems, A celebration of Jean-Pierre Gossez's 65th birthday, Bruxelles, Belgique, 2009.
- , Minimax algorithms: convergence and applications, New trends in scientific computing, Marseille, France, 2009.
- , Mountain Pass algorithm for some indefinite problems, New trends in scientific computing, Marseille, France, 2009.
Presentations & posters without abstract
- , Lane Emden problems : algorithm and symmetries, Matinée des chercheurs (MDC'2009), Mons, Belgique, 2009.
- , Delimited overloading, OCaml users meeting, Grenoble, France, 2009.
2008
Referenced Publications
- , On the asymptotics of solutions of the Lane-Emden problem for q-Laplacian, Archiv der Mathematik, 91 (2008), pp. 354–365, Birkhauser Verlag. DOI: 10.1007/s00013-008-2854-y.
- , Asymptotics and symmetries of least energy nodal solutions of Lane-Emden problems with slow growth, Communications in Contemporary Mathematics, 10 (2008), pp. 609–631, World Scientific Publishing Co.. DOI: 10.1142/S0219199708002910.
Publications (not referenced)
- , Analyse Mathématique I, course notes, 2008.
- , Quand les mathématiciens construisent des robots, Élement: le Magazine de l'Université de Mons, 1 (2008), pp. 26–27, Université de Mons.
Popularization
- , Atelier de robotique : Labyrinthe & Rubik's cube, 2008, Printemps des Sciences, UMONS, Mons.
- , Les experts à l'UMH, 2008, Atelier, UMONS, Mons.
Presentations & posters without abstract
- , Delimited Overloading, OCaml summer projects meeting, New-York, US-NY, 2008.
- , Lane Emden problem : algorithms, computation and symmetries, Oberseminar, Cologne, Allemagne, 2008.
2007
Publications (not referenced)
- , Introduction à la logique du premier ordre et à la théorie naïve des ensembles, course notes, 2007.
Popularization
- , Optimisation — quand les extrêmes sont les meilleurs, 2007, Printemps des Sciences, UMONS, Mons.
Presentations & posters with abstract
- , Lane Emden problem : algorithms and symmetries, PhD day 2007 (BMS), Bruxelles, Belgique, 2007.
- , Symmetry of least energy nodal solutions for the Lane-Emden problem, Variational and topological problems, Flagstaff, USA, 2007.
- , Algorithms and (partial) symmetry for solutions of the non-linear Poisson equation., Variational and topological problems, Flagstaff, USA, 2007.
- , Convergence of a mountain pass algorithm with projection, Theoretical and Computational nonlinear partial differential equations, Mexico city, Mexique, 2007.
2006
Popularization
- , Automates et atteignabilité, 2006, École secondaire de Waterloo, Waterloo.
Presentations & posters without abstract
- , Structure de la solution nodale d'énergie minimale, Séminaire d'analyse non-linéaire, Louvain-la-Neuve, Belgium, 2006.
2005
Publications (not referenced)
- , Mathématique Élémentaire, course notes, 2005.
Presentations & posters with abstract
- , Convergence of a mountain pass algorithm with projector., International Conference of Numerical Analysis and Applied Mathematics, Rhodes, Grèce, 2005.
2004
Referenced Publications
- , On O-Minimal Hybrid Systems, Lecture Notes in Computer Science, 2993 (2004), pp. 133–138, Springer.
Popularization
- , Préparer la transition secondaire-université dans les cours de mathématiques, 2004, Organisation d'une formation IFC, UMONS, Mons.
2002
Presentations & posters with abstract
- , Scalar- v.s. vector-recursion for BSS-recursive functions, Foundations of Computational Mathematics, Minneapolis, USA, 2002.
- , Equivalence of scalar- and vector-recursion for BSS machines, 21st Days of Weak Arithmetics, Saint Petersburg, Russie, 2002.
2001
Referenced Publications
- , Vector-Valued Variational Principles, Nonlinear Analysis: Theory, Methods and Applications, 52 (2001), pp. 197–218, Elsevier. DOI: 10.1016/S0362-546X(02)00103-7.
- , Equivalence of BSS scalar- and vector-recursion, Bulletin de la Société Mathématique de Belgique, A tribute to Maurice Boffa (2001), pp. 65–80, Hirsch.
Popularization
- , Catastrophes numériques, 2001, Brochure, UMONS.
2000
Referenced Publications
- , Isomorphism theorem for BSS recursively enumerable sets on real closed fields, Theoretical Computer Science, 231 (2000), pp. 253–273, Elsevier. DOI: 10.1016/S0304-3975(99)00103-6.
1998
Referenced Publications
- , Superlinear indefinite elliptic problems and Pohoz?aev type identities, Journal of Functional Analysis, 159 (1998), pp. 596–628, Elsevier. DOI: 10.1006/jfan.1998.3332.
Congress proceedings with peer-reviewing
- , Strongly indefinite variational problems with lack of compactness, International Conference on Differential Equations, Lisboa, Portugal, 1998.
- , Isomorphism Theorem for BSS Recursiveley Enumerable Sets over Real Closed Fields, International Colloquium Universal Machines and Computations, Metz, France, 1998.
Publications (not referenced)
- , Isomorphism theorem for BSS recursively enumerable sets on real closed fields, 1998, NeuroCOLT2.
1997
Referenced Publications
- , Problèmes elliptiques sur-linéaires avec non-linéarité sans signe défini, Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, 325 (1997), pp. 283–286, Elsevier Masson. DOI: 10.1016/S0764-4442(97)83956-0.
Books
- , Liouville type theorems and applications, 1997, Académie royale de Belgique. Classe des Sciences,.
1996
Referenced Publications
- , Extrema problems with critical Sobolev exponent on unbounded domains, Nonlinear Analysis: Theory, Methods and Applications, 26 (1996), pp. 823–833, Elsevier. DOI: 10.1016/0362-546X(94)00324-B.
- , Nontrivial solution of a semilinear Schrödinger equation, Communications in Partial Differential Equations, 21 (1996), pp. 1431–1449, Marcel Dekker. DOI: 10.1080/03605309608821233.
1994
Referenced Publications
- , Existence and Multiplicity Results for Homogeneous Second Order Differential Equations, Journal of Differential Equations, 112 (1994), pp. 239–249, Elsevier. DOI: 10.1006/jdeq.1994.1103.
