Parabolic-elliptic and parabolic systems in diffusion models

The presentation deals with nonlinear parabolic--elliptic and parabolic systems with initial-boundary conditions modeling biological ion channels and interdiffusion in solids. I will formulate theorems on local and global existence, uniqueness and properties of weak solutions, in suitable Sobolev spaces. Moreover,

finite implicit difference methods and theorems concerning existence and uniqueness of discrete solutions, and convergence and stability properties will be given. The agreement between theoretical results, numerical simulations and experiments in some cases will be shown.