Numerical Analysis Seminars: A one-dimensional model for cell adhesion, diffusion and chemotaxis
24 February 2012 14:00 in CG 83
We present a discrete model of cell motility in one dimension which incorporates the effects of volume filling and cell-to-cell adhesion. The continuum limit of the model is a nonlinear diffusion equation for the cell density, such that the diffusivity can turn negative if the adhesion coefficient is large. The consequent ill-posedness explains the pattern-forming behaviour observed in simulations of the underlying discrete model. The relationship between the discrete and continuum models is explored mathematically and numerically, and a Stefan-problem formulation of the continuum limit is proposed. Finally, we factor chemotaxis into the model, and show simulations of singular aggregation patterns arising from small initial data.
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