Can somebody point out a few references, book or paper, on how to solve a system of nonlinear PDEs which its geometry or domain changes with time?
For an example, suppose we have a diffusion-reaction system in which some molecules or proteins diffuse inside a circle and interact with some other molecules and proteins which are only on the surface of the circle. Because the circle represent a cell, the geometry or domain of the PDEs changes with time that is the domain increases with time.
Are there any books on how to solve PDE with time-dependent geometry?