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2009, Volume 25, Issue 1: 195-230. Doi: 10.3934/dcds.2009.25.195
This issue Previous Article Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff Next Article Periodic traveling waves of a mean curvature flow in heterogeneous media

Singular travelling waves in a model for tumour encapsulation

  • 1.

    Centre for Mathematical Medicine, School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD

  • 2.

    Centre for Mathematical Medicine, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD

Received:  July 31, 2007
Revised:  February 29, 2008
Published:  December 2008
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: Primary 92C50, 35M10; Secondary 92B05, 34C60.

    Citation:
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