All Outputs (3)

Non-local effects on travelling waves arising in a moving-boundary reaction-diffusion model (2022)
Journal Article
Fadai, N. T., & Billingham, J. (2022). Non-local effects on travelling waves arising in a moving-boundary reaction-diffusion model. Journal of Physics A: Mathematical and Theoretical, 55(40), Article 405701. https://doi.org/10.1088/1751-8121/ac8ef5

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
Fadai, N. T. (2023). Exact smooth and sharp-fronted travelling waves of reaction–diffusion equations with Weak Allee effects. Applied Mathematics Letters, 135, Article 108433. https://doi.org/10.1016/j.aml.2022.108433

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
Jepson, J. M., Fadai, N. T., & O’Dea, R. D. (2022). Travelling-Wave and Asymptotic Analysis of a Multiphase Moving Boundary Model for Engineered Tissue Growth. Bulletin of Mathematical Biology, 84(8), Article 87. https://doi.org/10.1007/s11538-022-01044-0

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.