Nonlinear diffusion in theory and applications: local and nonlocal models
Nonlinear diffusion in theory and applications. Local and nonlocal models
Prof. Juan Luis Vázquez (Universidad Autónoma de Madrid)
In this talk we we will present an overview of the mathematical theory of nonlinear diffusion with its typica free boundary problems, remarkable asymptotics and powerful numerics. We will then present the theory of nonlocal diffusion, mainly when modeled with fractional Laplacian operators, as it has been developed in the last decade: it has motivation in mechanics and probability, uses beautiful tools in analysis, and is full of open problems.