Nonlinear Diffusion Processes and their Intrinsic Regularity Theories

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Masterclass in Applied Nonlinear PDEs


Diffusion refers to a natural trend of equilibrium, balance, or spread of quantities in physical systems and models. Smoothing effects are among the most prominent features of such models with a broad array of applications. In this talk, I will describe the rich connections between the physical notion of diffusion and mathematical regularity estimates of solutions of the driving PDEs. I will be particularly interested in phenomena involving diffusion collapse and how this affects the intrinsic regularity theory of such models. 

Brief Biography

Eduardo Teixeira is a Full Professor in the Department of Mathematics at the University of Central Florida, USA. His research interests include free boundary problems and regularity theory for nonlinear partial differential equations. Among many distinctions, Prof. Teixeira received the 2013 Mathematical Congress of the Americas Prize and the 2017 ICTP-IMU Ramanujan Prize. He was elected permanent fellow of the Brazilian National Academy of Sciences in 2015 and awarded honorary citizenship of the State of Ceará in 2021.

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