Coffee Time: 15:30 - 16:00
I consider the vector counterpart of the classical p-Laplace and p-heat equations which are some of the building blocks for the mathematical description of non-linear plasticity, non-Newtonian fluids, and turbulent eddy viscosity models. I will discuss results of “natural regularity” and their role in the study of the well-posedness of the nonlinear pdes as well as in the theory of convergence for space-time discretisation methods. In particular, I will present the “A-approximation" method which generalises results by Necas and which reduces the problem to a family of linear ones.
Luigi C. Berselli received his master's degree in pure mathematics from Scuola Normale Superiore (SNS) in 1995 and his PhD in mathematics from the University of Pisa in 2000. He has been a full professor at the University of Pisa since 2016. His research expertise is in the mathematical theory and modeling of PDEs, particularly those that describe turbulent and non-Newtonian fluids. He has also collaborated with applied scientists on problems in engineering, robotics, medical science, and volcanology. He has published approximately 100 scientific papers and authored two books in the area of nonlinear PDEs.