Research Interests:
My research is broadly about the analysis (qualitative & quantitative) of Partial Differential Equations arising from applied domains. Some keywords are nonlocal PDEs, kinectic theory, hypocoercivity, cross-diffusion systems, structured population dynamics in mathematical biology.
Below are some of my publications grouped under some of these categories. The full list of my publications can be found here.
Hypocoercivity and scaling limits in kinetic theory
J. Evans, D. Morris, H.Y., On a class of nonlinear BGK-type kinetic equations with density dependent collision rates (2025).
H.Y, On quantitative hypocoercivity estimates based on Harris-type theorems (2023).
J. A. Cañizo, C. Cao, J. Evans, H.Y, Hypocoercivity of linear kinetic equations via Harris's Theorem, (2020).
Kinetic theory in mathematical biology
J. Evans, H.Y, Trend to equilibrium for run and tumble equations with non-uniform tumbling kernels (2024).
J. Evans, H.Y, On the asymptotic behaviour of a run and tumble equation for bacterial chemotaxis, (2023).
Derivation of continuum equations (via tools used in kinetic theory )
S. Merino-Aceituno, S. Plunder, C. Wytrzens, H.Y, Macroscopic effects of an anisotropic Gaussian-type repulsive potential: nematic alignment and spatial effects (2025).
Asymptotic behaviour of PDE models in population dynamics (mathematical biology)
J. A. Cañizo, P. Gabriel, H.Y, Spectral gap for the growth-fragmentation equation via Harris's Theorem (2021).
J. A. Cañizo, H.Y, Asymptotic behaviour of neuron population models structured by elapsed-time (2019).
Cross-diffusion PDE systems
R. Ducasse, F. Santambrogio, H.Y, A cross-diffusion system obtained via (convex) relaxation in the JKO scheme (2023).
A. B. T. Barbaro, N. Rodriguez, H.Y, N. Zamponi, Analysis of a cross-diffusion model for rival gangs interaction in a city (2021).
Structure-preserving numerical schemes
V. Calvez, H. Hivert, H.Y, Concentration in Lotka-Volterra parabolic equations: an asymptotic-preserving scheme (2023).
You can access my
ORCiD profile (ORCiD: 0000-0001-7545-1891),
Web of Science profile (Researcher iD: AAV 3380 2020),
Referee activity:
I have reviewed for
Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire
Physica D: Nonlinear Phenomena
SIAM Journal on Mathematical Analysis
Acta Aplicandae Mathematicae
Kinetic and Related Models
Mathematical Models and Methods in Applied Sciences
Nonlinear Analysis
Differential Equations and Dynamical Systems
Membership:
AMS: American Mathematical Society (2025 - ongoing)
ESMTB: European Society of Mathematical and Theoretical Biology (2024 - ongoing)
EMS: European Mathematical Society (2024 - ongoing)
EWM-NL: European Women in Mathematics, The Netherlands (2022 - ongoing)
EWM: European Women in Mathematics (2020 - ongoing)
SIAM: Society of Industrial and Applied Mathematics (2022)