Séance Séminaire

Séminaire ACSIOM

Patterns on evolving surfaces.

The Schnakenberg model is commonly used to model the emergence of patterns on the animal skin. The model is quite challenging both analytically and numerically because it is a nonlinear system of PDE and usually the computational domain evolves with time. To model the growth of the organsim we consider it to be topologically a sphere whose Riemannian metric depends on time. In our approach we can quite conveniently describe a large class of surfaces. Once the appropriate framework is established we can then use finite elements to compute the solution. We also analyze the relationship between the eigenfunctions of the Laplacian and the patterns observed.