Multi-phase Stefan problems for a nonlinear 1-d model of cell-to-cell adhesion and diffusion

Details Multi-phase Stefan problems for a nonlinear 1-d model of cell-to-cell adhesion and diffusion Multi-phase Stefan problems for a nonlinear 1-d model of cell-to-cell adhesion and diffusion

2009-02-26

arxiv.org/abs/0902.4561v2

Eur. J. Appl. Math. 21(2), 109-136 (2010)

Mathematics

Analysis of PDEs

'O(h)' typo on p.2 fixed

Scientific paper

We consider a family of multi-phase Stefan problems for a certain 1-d model of cell-to-cell adhesion and diffusion, which takes the form of a nonlinear forward-backward parabolic equation. In each material phase the cell density stays either high or low, and phases are connected by jumps across an `unstable' interval. We develop an existence theory for such problems which allows for the annihilation of phases and the subsequent continuation of solutions. Stability results for the long-time behaviour of solutions are also obtained, and, where necessary, the analysis is complemented by numerical simulations.

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