Dr Alexandra Holzinger
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Rigorous derivation of population cross-diffusion systems from moderately interacting particle systems
Li Chen, Esther Daus, Alexandra Holzinger and Ansgar Jüngel. Journal of Nonlinear Science 31 (2021): 1-38.
Analysis and mean-field derivation of a porous-medium equation with fractional diffusion
Li Chen, Alexandra Holzinger, Ansgar Jüngel and Nicola Zamponi. Communications in Partial Differential Equations 47.11 (2022): 2217-2269.
A comprehensive algorithm for estimating lithium-ion battery parameters from measurements
Dominik Dvorak, Thomas Bäuml, Alexandra Holzinger, and Hartmut Popp. IEEE Transactions on Sustainable Energy 9.2 (2017): 771-779.
My research focuses on the connection between (stochastic) interacting microscopic particle models and non-linear partial differential equations which represent the corresponding macroscopic levels.
In particular, I am interested in questions which arise naturally when dealing with micro/macro connections like well-posedness of the underlying non-linear PDEs, connections between different convergence types of the particles systems and fluctuations around the macroscopic description. Additionally, I am interested in applications of those mathematical concepts to frameworks coming from biology or neuroscience.