PDE Models and Nonlinear Dynamics

My research involves mathematical analysis and simulation of partial differential equation (PDE) models inspired by biology. For example, reaction–diffusion systems are prototype PDE models used to explain collective cell movement. I apply analytical techniques including travelling-wave analysis and stability analysis to investigate the properties of these models. In addition, many biological processes can be modelled using PDEs on moving domains of arbitrary shape. I apply numerical methods, especially the level-set method, to solve these problems.

Collaborators

• Tom Miller (PhD Student, UniSA)
• Bronwyn Hajek
• Mat Simpson
• Dietmar Oelz
• Nizhum Rahman
• Ben Binder
• Ed Green
• Sanjeeva Balasuriya
• Robby Marangell
• Martin Wechselberger

Key Publications

• Pattern formation and front stability for a moving-boundary model of biological invasion and recession, Physica D (2023)
• The effect of geometry on survival and extinction in a moving-boundary problem motivated by the Fisher-KPP equation, Physica D (2022)
• Nutrient-limited growth with non-linear cell diffusion as a mechanism for floral pattern formation in yeast biofilms, J. Theor. Biol. (2018)
• Predicting channel bed topography in hydraulic falls, Phys. Fluids (2015)
• Survival, extinction, and interface stability in a two-phase moving boundary model of biological invasion., Physica D (2023)