Research Interests:
- Analysis of PDEs
- Well-posedness and long-time assymptotic analysis
- Kinetic equations in bounded domains
- Kinetic problems in non-equilibrium settings
- kinetic Fokker-Planck, Boltzmann, Landau, and Vlasov-Poisson Boltzmann equations
- Perturbation theory
- Semigroup theory
- Hypocoercivity theory
- Krein-Rutmann and Doblin-Harris theorems
List of Publications:
- The Boltzmann equation with non-isothermal Maxwell boundary conditions. 2026. Preprint arxiv, HAL.
- The Boltzmann equation on smooth and cylindrical domains with Maxwell boundary conditions. 2025. Preprint arxiv, HAL.
- Evans, J., Medina, R. Existence and Stability of Non-Equilibrium Steady States of a Weakly Non-Linear Kinetic Fokker-Planck Equation in a Domain. J Stat Phys 193, 47 (2026). DOI, arXiv, HAL.
- Constructive Krein-Rutman result for Kinetic Fokker-Planck equations in a domain. 2024. In collaboration with K. Carrapatoso, P. Gabriel, S. Mischler. Preprint arXiv.
Research Experience:
Invited Talks at Conferences and Seminars:
- Brief introduction to the Boltzmann equation. Young Researchers Seminar, at Université Paris Dauphine - PSL, Paris, France. Jan. 2025.
- Constructive Krein-Rutman result for kinetic Fokker-Planck equations in a domain (joint work with K. Carrapatoso, P. Gabriel and S. Mischler). Presentation at the Junior Analysis Seminar at Imperial College London, UK. Oct. 2024.
- The Boltzmann equation on C^1 and cylindrical domains near the hydrodynamic limit. Presentation at the Partial Differential Equations and their Applications Seminar at the University of Warwick, UK. Oct. 2024.
- The Boltzmann equation in a cylinder near the hydrodynamic limit. Conference “Analysis of PDEs in Mathematical Physics”, at University of Bath, UK. Jun. 2024.
- Introduction to the kinetic Fokker-Planck equation and its long-time behavior. Young Researchers Seminar, at Université Paris Dauphine - PSL, Paris, France. Nov. 2023.
- Hypocoercivity estimates for some linearized kinetic operators. Young Researchers Seminar, at Université de Lille, France. May. 2023.
- Hypocoercivity estimates for some linearized kinetic operators. Young Researchers Seminar, at Université Paris Dauphine - PSL, Paris, France. Mar. 2023.
- 'Cause I'll L-ove you to-infinity estimates for the Boltzmann equation. MAFRAN Days, at King's College, Cambridge, UK. Feb. 2023.
- Fixed points in non-expansives maps. International Congress COMPUMAT 2019, at La Habana, Cuba. Jun. 2019.
- Extrapolation Methods for Approximating a Fairness Functional. International Workshop on Operations Research (IWOR), at La Habana, Cuba. Mar. 2019.
- Restriction-based interpolation with cubic A-splines. International Conference on Operations Research (ICOR), at La Habana, Cuba. Mar. 2018.
Poster Presentations:
- Constructive Krein-Rutman result for kinetic Fokker-Planck equations in a domain (joint work with K. Carrapatoso, P. Gabriel and S. Mischler). Poster presentation at the summer school “Collective behavior and Pattern formation”, CIRM, Marseille, France. Jul. 2024.
- Constructive Krein-Rutman result for kinetic Fokker-Planck equations in a domain (joint work with K. Carrapatoso, P. Gabriel and S. Mischler). Poster presentation at the summer school “Frontiers in Interacting Particle Systems, Aggregation-Diffusion Equations & Collective Behavior ”, CIRM, Marseille, France. Jun. 2024.
Participation on Conferences, Workshops and Schools:
- Summer school - Collective behavior and Pattern formation, at CIRM, Marseille, France. Jul. 2024
- Research school - Frontiers in Interacting Particle Systems, at CIRM, Marseille, France. Jun. 2024
- Research School - Kinetic Theory, at CIRM, Marseille, France. Nov. 2022
- Conference - When Kinetic Theory Meets Fluid Mechanics, at FIM, ETH Zürich, Switzerland. Jul. 2022
- CIMPA Research Summer School - Mathematical Models in Biology and Related Applications of Partial Differential Equations, at Universidad de La Habana, Cuba. Jun. 2019
- III Winter School in Computer Science, at Universidad de La Habana, Cuba. Mar. 2019
