Curvature dependence of reaction-diffusion wave front speed with nonlinear diffusion.

Overview

Reaction-diffusion waves describe the progression in space of wildfires, species invasions, epidemic spread, and biological tissue growth. When diffusion is linear, these waves are known to advance at a rate that strongly depends on the curvature of the wave fronts. How nonlinear diffusion affects the curvature dependence of the progression rate of these wavefronts remains unknown.

Research activities

You will use partial differential equation analyses and numerical simulations to investigate the propagation in space of wavefronts of different shapes for a variety of nonlinear diffusion functions. Results will be compared with recent works that exhibit several curvature-dependent contributions to the progression rate of wavefronts when diffusion is linear.

Outcomes

An increased understanding of how reaction-diffusion wavefronts propagate in restricted spaces constraining their shape when diffusion is nonlinear, with application to biological tissue growth in porous scaffolds.

Skills and experience

This project can be tailored to suit research students at VRES, Honours, Masters, and PhD level. Some proficiency in differential equations and computer modelling is expected.

Keywords

• mathematical modelling
• numerical simulation
• partial differential equation (PDE)
• asymptotic analyses

Contact

Contact the supervisor for more information.