Jean Cauvin-Vila

Jean Cauvin-Vila

Ph.D student since September 2020:

This Ph.D thesis is concerned with the mathematical modelling, analysis and control of some cross-diffusion systems in moving domains. Cross-diffusion systems are strongly coupled degenerate parabolic systems that appear in the modelling of multicomponent diffusive systems, with applications in physics, chemistry and population dynamics. Their analysis relies mostly on the “entropy structure” of specific systems, which provides a Lyapunov functional and a formal gradient flow framework. This Ph.D thesis focuses on cross-diffusion systems defined in time-dependent domains arising in materials science. One significant goal is the modelling and analysis of a two-phase model with a free boundary at the interface for the modelling of a Physical Vapor Deposition process for solar cells fabrication.

I am funded by the ANR Project COMODO of Virginie Ehrlacher:

SupervisorVirginie Ehrlacher (CERMICS, ENPC)

Institutions: CERMICS, Ecole Nationale des Ponts et Chaussées and Inria, team MATHERIALS.


CERMICS – ENPC     Bâtiment Coriolis B312
6 et 8 avenue Blaise Pascal
Cité Descartes – Champs sur Marne
77455 Marne la Vallée Cedex 2 (FRANCE)

CV: CV_eng

Scientific activity
  • Papers:
    – with Virginie Ehrlacher and Amaury Hayat, Boundary stabilization of one-dimensional cross-diffusion systems in a moving domain: linearized system,  accepted for publication in Journal of Differential Equations, 2022. preprint
  • Talks:
    – September 2020. Nonlinear evolutionary equations and applications, TU Chemnitz. A cross-diffusion Cahn-Hilliard system: existence and numerics. slides 
    – June 2022. CANUM, Evian-les-bains. Backstepping boundary stabilization of a cross-diffusion system in a moving domain: linearized system. slides
    – October 2021. Congrès des jeunes chercheurs en mathématiques appliquées (CJC-MA), Ecole Polytechnique. Cross-diffusion and boundary stabilization by backstepping. slides
    – June 2021. Day of the doctoral school MSTIC, virtual. Introduction to diffusion, cross-diffusion and a stabilization problem to an audience of graduate students from different fields. slides
    – November 2020. Day of the new Ph.D students at CERMICS, virtual. Introduction to my Ph.D project to an audience of young applied mathematicians. slides
  • Posters:
    – June 2021. Congrès SMAI, La Grande-Motte. “Boundary stabilization of a cross-diffusion system in a time-dependent domain using backstepping“. Poster_SMAI_2021
Teaching activity
  • 2022-2023:
    – In charge of one group in the class “Analysis and scientific computing” at Ecole des Ponts.
  • 2021-2022:
    – In the spring semester, I am in charge of a group in the class “Partial differential equations: variational approaches” under the coordination of Frédéric Legoll. I teach lectures and exercise sessions about Sobolev spaces, weak formulation of elliptic PDEs, applications in continuum mechanics and introduction to the calculus of variations.
    In the fall semester, I am occasionaly involved in the class “Analysis and scientific computing (AnaCS)” under the coordination of Gabriel Stoltz. It is a course for first-year students at Ecole des Ponts, taught in flipped classrooms. Topics include measure theory and integration, Fourier series and transform, distributions theory, PDEs and finite difference methods…
     In the fall semester, I am in charge of the exercise sessions of a group in the class “Introduction to optimization (OPTI)” under the coordination of Frederic Meunier. It is a course for first-year students at Ecole des Ponts. Topics include modelling, existence theory and optimality conditions in finite dimension, convexity, linear programming, algorithms…
    – In September 2021, I am in charge of a group in the intensive class “Outils Mathématiques Pour l’Ingénieur (OMPI)” under the coordination of Antoine Levitt. The class is designed for first-year students at Ecole des Ponts and consists in mini-lectures and exercice sessions in small groups around Banach spaces, calculus and ordinary differential equations. Visit
  • 2020-2021:
    – In the spring semester, I am in charge of the exercise sessions of a group in the class MA210 “Analyse Fonctionnelle” at Sorbonne Université, under the coordination of Frédéric Klopp and Fabrice Planchon. This class aims at presenting the bases of functional and real analysis to 3rd year bachelor students.

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