First Year's Courses (I)
Lorenzo Giacomelli is Full Professor of Mathematical Analysis at the School of Engineering in Sapienza. At the same school, he has been Assistant Professor from 1999 to 2005 and Associate Professor from 2005 to 2021. He graduated in Mathematics in 1995 (U. Florence) and obtained a PhD in Mathematics in 2000 (Sapienza). He has taken part in National and European research projects (PRIN, TMR, RTN, ITN) and he has coordinated National and local ones (GNAMPA, Sapienza). He has tought post-graduate courses at SISSA (Trieste), the University of Bonn, and Sapienza. He has visited various scientific institutions, among which IPAM (Los Angeles), PIMS (Vancouver), BIRS (Banff), MPI-MIS (Leipzig), Fields Institute (Toronto), and the universities of Valencia, Bonn, Koln, Warsaw, and California at Berkeley. Lists of his publications and invited lectures are available on this site.
He is mainly interested in the mathematical analysis of nonlinear partial differential equations (PDEs), with a focus on the interplay with applications: the collaboration with experts during the development of the model, the analysis of solutions' behavior with respect to questions which naturally stem from the phenomenon described by the model, and the feed-back of the results. In particular, he has been working on (systems of) degenerate parabolic PDEs -arising from fluid dynamics, material science, and image processing- in which presence of multiple scales and/or the evolution of interfaces and singularities play an essential role: "thin-film" type equations, Hele-Shaw flows, Cahn-Hilliard type equations, the Kuramoto-Sivashinsky equation, gradient plasticity theories, 1-harmonic flows on manifolds, flux-saturated diffusion equations, and forward-backward parabolic equations. In these frameworks, his contributions mainly concern well-posedness (existence, uniqueness, non-uniqueness phenomena, regularity of solutions) and qualitative behaviour of solutions (asymptotics, scaling laws, evolution of interfaces and singularities).