Finite speed of propagation for a non-local porous medium equation

TL;DR

This paper proves that solutions to certain non-local porous medium equations do not propagate instantaneously but instead have a finite speed, using adapted methods from previous research by Caffarelli and Vázquez.

Contribution

It introduces a novel adaptation of existing techniques to establish finite speed of propagation for non-local porous medium equations.

Findings

Solutions exhibit finite speed of propagation.

Method successfully adapts previous arguments to non-local equations.

Provides theoretical proof of propagation speed property.

Abstract

This note is concerned with proving the finite speed of propagation for some non-local porous medium equation by adapting arguments developed by Caffarelli and V\'azquez (2010).