Title: An Introduction to the Porous Medium Equation

 

 

Abstract: In this talk, we will explore the Porous Medium Equation, which appears in the description of different natural phenomenon as related to diffusion, filtration, or heat propagation. We will compare it with the heat equation, introduce the Barenblatt profile, and discuss the appearance of free boundary (a consequence of the finite propagation property), the comparison principle, and the Aronson-Benilan estimate. If time allows, its application in the Keller-Segel model will be discussed along with some open questions.