Recent advances in doubly nonlinear equations

Overview

Abstract

The term doubly nonlinear refers to the fact that the diffusion part depends nonlinearly both on the gradient and the solution itself. Such equations describe several physical phenomena and were introduced by Lions and Kalashnikov. These equations have an intrinsic mathematical interest because they represent a natural bridge between the more natural generalizations of the heat equation: the p-Laplacian and the porous medium equation. Especially in the last few years, many papers have been devoted to this topic. The idea is to give a unified approach that is comprehensive of the porous medium and the p-Laplacian equations. The strategies are sometimes not rigorous, sometimes not with sharp assumptions or with unnecessary long proofs. In this talk, I will discuss the state-of-the-art, my contributions, and open questions.

Brief Biography

Vincenzo Vespri is a Full Professor of Mathematics at the University of Florence, where he teaches Mathematical Analysis, Probability and Statistics, Blockchain Technology, and Mathematical Finance in various undergraduate and Masters courses. He is also an advisor for the Minister of Education and Merit for teaching STEAM subjects and is a member of the self-evaluation group of the University of Salerno. He was Sherpa for the G7 and G20 for the Italian Ministry of Education, University and Research. His main research areas concern the structural properties of elliptic and parabolic equations, blockchain technology, and the relationship between Mathematics and Dante Alighieri's Comedy. He is the author of more than 150 publications on these topics.