Nonlinear Diffusion Equations -An Overview

I present an overview of the topic of nonlinear diffusion equations in divergence form, with a special focus on equations exhibiting double nonlinearity. We acquaint ourselves with various equations, their applications and the mathematically relevant questions such as the existence, uniqueness and regularity of solutions. I also present some recent results concerning strongly anisotropic diffusion equations where tools from regularity theory also play a central role in the proof of the existence of solutions to a suitably formulated Cauchy-Dirichlet problem.