All Outputs (3)

Non-local effects on travelling waves arising in a moving-boundary reaction-diffusion model (2022)
Journal Article

We examine travelling wave solutions of the partial differential equation u_t = u_xx + u(1 − u * φ) on a moving domain x ≤ L(t), where u * φ is the spatial convolution of the population density with a kernel φ(y). We provide asymptotic approximations... Read More about Non-local effects on travelling waves arising in a moving-boundary reaction-diffusion model.

Exact smooth and sharp-fronted travelling waves of reaction–diffusion equations with Weak Allee effects (2022)
Journal Article

We provide new exact forms of smooth and sharp-fronted travelling wave solutions of the reaction–diffusion equation, ∂tu=R(u)+∂xD(u)∂xu, where the reaction term, R(u), employs a Weak Allee effect. The resulting ordinary differential equation system i... Read More about Exact smooth and sharp-fronted travelling waves of reaction–diffusion equations with Weak Allee effects.

Travelling-Wave and Asymptotic Analysis of a Multiphase Moving Boundary Model for Engineered Tissue Growth (2022)
Journal Article

We derive a multiphase, moving boundary model to represent the development of tissue in vitro in a porous tissue engineering scaffold. We consider a cell, extra-cellular liquid and a rigid scaffold phase, and adopt Darcy’s law to relate the velocity... Read More about Travelling-Wave and Asymptotic Analysis of a Multiphase Moving Boundary Model for Engineered Tissue Growth.