In the talk, I will describe an abstract framework for non-local
non-linear diffusion, by which we mean a phenomenon with properties strongly
associated to diffusive processes such as the conservation of
mass, the maximum principle, and the comparison principle. This
framework encompasses some of the known
examples of equations like the fractional porous medium equation
or the equation with the fractional $p$-Laplacian, but it also
opens up the space for new examples to be
constructed and studied.
The existence, uniqueness and other fundamental properties of
solutions for the Cauchy problem for such a general equation
have been shown.
This is a joint work with Milosz Krupski and Moritz Kassmann.