The mathematical theories of diffusion. Nonlinear and fractional diffusion

Understand

We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research.

• The linear heat equation is the basic mathematical model that has been thoroughly studied in the last two centuries.
• It was followed by the theory of parabolic equations of different types.
• In a parallel development, the theory of stochastic differential equations gives a foundation to the probabilistic study of diffusion.