Cookies on this website

We use cookies to ensure that we give you the best experience on our website. If you click 'Accept all cookies' we'll assume that you are happy to receive all cookies and you won't see this message again. If you click 'Reject all non-essential cookies' only necessary cookies providing core functionality such as security, network management, and accessibility will be enabled. Click 'Find out more' for information on how to change your cookie settings.

In this paper we study an existing mathematical model of tumour encapsulation comprising two reaction-convection-diffusion equations for tumour-cell and connective-tissue densities. The existence of travelling-wave solutions has previously been shown in certain parameter regimes, corresponding to a connective tissue wave which moves in concert with an advancing front of the tumour cells. We extend these results by constructing novel classes of travelling waves for parameter regimes not previously treated asymptotically; we term these singular because they do not correspond to regular trajectories of the corresponding ODE system. Associated with this singularity is a number of further (inner) asymptotic regions in which the dynamics is not governed by the travelling-wave formulation, but which we also characterise.

Original publication




Journal article


Discrete and Continuous Dynamical Systems

Publication Date





195 - 230