Abstract

We are interested in the effect of the nonlinearities on the emergence of non trivial patterns in several differential models arising in physics and other sciences. Such self organized structures correspond to selected solutions of the differential problem, possessing some special symmetries or shadowing particular shapes. We wish to understand the main analytical mechanisms involved in this process in terms of the common variational structure of the problems. A feature of this project rests indeed in the interchange of attack strategies between different specific applications in the fields of partial differential equations and systems and Hamiltonian systems. There is a remarkable unity in methodology across the different parts of the project. On the other hand, all the proposed issues must be addressed in interdisciplinary spirit and require expertise in several fields of mathematics: variational and topological methods, qualitative and regularity theory for PDE’s and free boundary problems, Morse and Critical Point theory, equivariant topology, geometric measure theory.

Partenariato

• Università degli Studi di Torino (PI)
• Università degli Studi “La Sapienza” di Roma
• Politecnico di Milano
• Università degli Studi di Milano-Bicocca
• Università degli Studi di Bologna

Importo del progetto

Importo totale del progetto        Euro 192.180
Importo del progetto Uniud        Euro 30.000
Finanziamento Uniud                Euro 800

Durata

• Data avvio progetto 28/09/2023
• Data conclusione progetto 28/09/2025