Partial differential equations on and for evolving surfaces occur in many applications.
For example, traditionally they arise naturally in fluid dynamics and materials
science and more recently in the mathematics of images.
In this talk we describe computational approaches to the formulation and
approximation of transport and diffusion of a material quantity on an
evolving surface.
We also have in mind a surface which not only evolves in the normal direction
so as to define the surface evolution but also has a tangential velocity
associated with the motion of material points in the surface which advects material
quantities such as heat or mass.This is joint work with G. Dziuk