Billel Guelmame

Postdoctoral associate at École Normale Supérieure de Lyon, working with Julien Vovelle.

Unité de Mathématiques Pures et Appliquées, ENS Lyon
46, allée d'Italie, Lyon, France
billel.guelmame@ens-lyon.fr
orcid.org/0000-0003-0711-4927
researchgate.net/profile/Billel-Guelmame
scholar.google.com/citations?user=sfPv708AAAAJ

My research

My research interests lie in the analysis of both deterministic and stochastic nonlinear partial differential equations. Specifically, I work on the regularity of entropy solutions for certain nonlinear hyperbolic equations within fractional BV spaces. Additionally, my interests extend to the study of perturbations of hyperbolic equations and their singular limits. Interestingly, the watery theme in my name, Billel¹ Guelmame², seems to be in perfect accord with my research. I also find myself immersed in water-wave problems, particularly within the shallow-water regime.

I am also open to working on other equations and to expanding my research area. Please feel free to contact me for possible collaborations and/or discussions!

Journal Papers

1. B. Guelmame and J. Vovelle. Global dissipative martingale solutions to the variational wave equation with stochastic forcing.
   arXiv   hal   Stochastics and Partial Differential Equations. (2024)  


2. B. Guelmame and H. Houamed. Convergence rate for a regularized scalar conservation law.
   arXiv   hal   Zeitschrift für Angewandte Mathematik und Physik. (2024)  


3. B. Guelmame. On a Hamiltonian regularization of scalar conservation laws.
   arXiv   hal   Discrete Contin. Dyn. Syst. A. (2024)  


4. B. Guelmame. Global weak solutions of the Serre–Green–Naghdi equations with surface tension.
   arXiv   hal   Annales de l'Institut Henri Poincaré C, Analyse non linéaire. (2023)


5. B. Guelmame. On the blow-up scenario for some modified Serre–Green–Naghdi equations.
   arXiv   hal   Nonlinear Analysis. (2022)


6. B. Guelmame, D. Clamond and S. Junca. Local well-posedness of a Hamiltonian regularisation of the Saint-Venant system with uneven bottom.
   arXiv   hal   Methods and Applications of Analysis. (2022)


7. B. Guelmame, S. Junca, D. Clamond and R.L. Pego. Global weak solutions of a Hamiltonian regularised Burgers equation.
   arXiv   hal   J. Dynam. Differential Equations. (2022)


8. C. Bourdarias, A.P. Choudhury, B. Guelmame and S. Junca. Entropy solutions in BV^s for a class of triangular systems involving a transport equation.
   arXiv   hal   SIAM J. Math. Anal. (2022)


9. B. Guelmame, D. Clamond and S. Junca. Hamiltonian regularisation of the unidimensional barotropic Euler equations.
   arXiv   hal   Nonlinear Anal. Real World Appl. (2022)


10. S. Ghoshal, B. Guelmame, A. Jana and S. Junca. Optimal regularity for all time for entropy solutions of conservation laws in BV^s.
    arXiv   hal   Nonlinear Differential Equations Appl. (2020)


11. B. Guelmame, S. Junca and D. Clamond. Regularizing effect for conservation laws with a Lipschitz convex flux.
    arXiv   hal   Commun. Math. Sci. (2019)