##### Department of Mathematics,

University of California San Diego

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### Informal Seminar on Mathematics and Biochemistry-Biophysics

## Leonard M. Sander

#### University of Michigan, Ann Arbor \\ Physics Department

## A generalized Cahn-Hilliard equation for biological applications

##### Abstract:

We study fronts of cells such as those invading a wound or in a growing tumor. First we look at a discrete stochastic model in which cells can move, proliferate, and experience cell-cell adhesion. We compare this with a coarse-grained, continuum description of this phenomenon by means of a generalized Cahn-Hilliard equation (GCH) with a proliferation term. There are two interesting regimes. For subcritical adhesion, there are propagating "pulled" fronts, similarly to those of Fisher-Kolmogorov equation. The problem of front velocity selection is examined, and our theoretical predictions are in a good agreement with a numerical solution of the GCH equation. For supercritical adhesion, there is a nontrivial transient behavior. The results of continuum and discrete models are in a good agreement with each other for the different regimes we analyzed.

Hosts: Li-Tien Cheng and Bo Li

### April 14, 2009

### 2:00 PM

### AP&M 5829

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