Partial differential equations (PDEs) describe phenomena in physics and biology including diffusion of particles and the motion of fluids. I have studied a variety of problems related to PDE models, including in shallow water waves, moving-boundary problems in population biology, and non-standard reaction—diffusion models.
Publications
- AKY Tam, Z Yu, RM Kelso and BJ Binder, Predicting channel bed topography in hydraulic falls, Phys. Fluids 27 (2015), 112106, DOI: 10.1063/1.4935419.
- AKY Tam and MJ Simpson, The effect of geometry on survival and extinction in a moving-boundary model motivated by the Fisher—KPP equation, Physica D 438 (2022), 133305, DOI: 10.1016/j.physd.2022.133305.
- AKY Tam and MJ Simpson, Pattern formation and front stability in a moving-boundary model of biological invasion and recession, Physica D 444 (2023), 133593, DOI: 10.1016/j.physd.2022.133593.
- MJ Simpson, N Rahman, SW McCue and AKY Tam, Survival, extinction, and interface stability in a two-phase moving boundary model of biological invasion, Physica D 456 (2023), 133912 DOI: 10.1016/j.physd.2023.133912.
- T Miller, AKY Tam, R Marangell, M Wechselberger and BH Bradshaw-Hajek, Analytic shock-fronted solutions to a reaction—diffusion equation with negative diffusivity, Stud. Appl. Math. 153 (2024), e12685, DOI: 10.1111/sapm.12685.
- MJ Simpson, N Rahman and AKY Tam, Front stability of infinitely steep travelling waves in population biology, J. Phys. A 57 (2024), 315601, DOI: 10.1088/1751-8121/ad6223.
- T Miller, AKY Tam, R Marangell, M Wechselberger and BH Bradshaw-Hajek, Shock selection in reaction-diffusion equations with partially negative diffusivity using nonlinear regularisation, arXiv, DOI: 10.48550/arXiv.2410.04106.
Collaborators