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
2019
Popularization
- , Optimisation — Quand les extrêmes sont les meilleurs !, 2019, Collège Saint Guibert, Gembloux.
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.
- , A non-variational system involving the critical Sobolev exponent. The radial case., Journal d'analyse mathématique, (2018), Hebrew University Magnes Press. arXiv: 1603.05641.
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
- , 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. 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 & Applications, (2016), pp. 236–273, Elsevier Science. 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 Science. arXiv: 1407.4029, DOI: 10.1016/j.nonrwa.2015.06.001.
- , Nodal properties of eigenfunctions of a generalized buckling problem on balls, Positivity, (2015). 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, South West Texas State University. 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, USA, 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. arXiv: 1205.0517.
- , 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, Nonlinear Differential Equations and Applications, 20 (2013), pp. 511–521.
- , Lane-Emden problems: Asymptotic behavior of low energy nodal solutions, Annales de L'Institut Henri Poincaré. Analyse Non Linéaire, 30 (2013), pp. 121–140, Gauthier-Villars.
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 & Applied Mathematics, 236 (2012), pp. 2025–2036, Elsevier Science. 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, Element : 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, South West Texas State University. 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, Differential and Integral Equations.
- , Nodal line structure of least energy nodal solutions for Lane-Emden problems, Comptes Rendus. Mathématique, 347 (2009), pp. 767–771, Elsevier Science. 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 [=ADM], 91 (2008), Springer. 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 Company. DOI: 10.1142/S0219199708002910.
Publications (not referenced)
- , Analyse Mathématique I, course notes, 2008.
- , Quand les mathématiciens construisent des robots, Element : 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, USA, 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), 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, St. Petersburg, Russie, 2002.
2001
Referenced Publications
- , Vector-Valued Variational Principles, Nonlinear Analysis: Theory, Methods & Applications, 52 (2001), Elsevier Science. 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), 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), Elsevier Science. 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), Academic Press. 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), 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 & Applications, 26 (1996). DOI: 10.1016/0362-546X(94)00324-B.
- , Nontrivial solution of a semilinear Schrödinger equation, Communications in Partial Differential Equations, 21 (1996), Taylor & Francis Ltd. DOI: 10.1080/03605309608821233.
1994
Referenced Publications
- , Existence and Multiplicity Results for Homogeneous Second Order Differential Equations, Journal of Differential Equations, 112 (1994), Academic Press. DOI: 10.1006/jdeq.1994.1103.
