University of Heidelberg, **Applied Analysis Seminar**

Prof. Grzegorz Karch (Institute of Mathematics, University of Wroclaw)

On a nonlinear nonlocal diffusion equation

*INF 205, SR1*

On a nonlinear nonlocal diffusion equation

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.

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