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ERC - Complex Patterns for Strongly Interacting Dynamical Systems

Complex Patterns for Strongly Interacting Dynamical Systems

Tipologia
Progetti internazionali
Programma di ricerca
ERC Advanced Grant 2013
Ente finanziatore
Unione Europea attraverso il European Research Coucil (ERC)
Budget
1,345,000
Periodo
01/02/2014 - 31/01/2019
Coordinatore
Prof. Susanna Terracini

Aree / Gruppi di ricerca

Partecipanti al progetto

Descrizione del progetto

ERC Advanced Grant Project 2013 – N. 339958

Complex Patterns for Strongly Interacting Dynamical Systems - COMPAT
Duration: 5 years (starting February 2014)
Principal Investigator: Susanna Terracini
 
This project focuses on nontrivial solutions of systems of differential equations characterized by strongly nonlinear interactions. We are interested in the effect of the nonlinearities on the emergence of non trivial self-organized structures. Such patterns correspond to selected solutions of the differential system possessing special symmetries or shadowing particular shapes. We want to understand, from the mathematical point of view, what are the main mechanisms involved in the aggregation process in terms of the global variational structure of the problem. Following this common thread, we deal with both with the classical N-body problem of Celestial Mechanics, where interactions feature attractive singularities, and competition-diffusion systems, where pattern formation is driven by strongly repulsive forces. More precisely, we are interested in periodic and bounded solutions, parabolic trajectories with the final intent to build complex motions and possibly obtain the symbolic dynamics for the general N–body problem. On the other hand, we deal with elliptic, parabolic and hyperbolic systems of differential equations with strongly competing interaction terms, modeling both the dynamics of competing populations (Lotka- Volterra systems) and other interesting physical phenomena, among which the phase segregation of solitary waves of Gross-Pitaevskii systems arising in the study of multicomponent Bose-Einstein condensates. In particular, we will study existence, multiplicity and asymptotic expansions of solutions when the competition parameter tends to infinity. We shall be concerned with optimal partition problems related to linear and nonlinear eigenvalues
We want to understand, from the mathematical point of view, what are the main mechanisms involved in the aggregation process in terms of the global variational structure of the problem.
Therefore we will consider cases where
(a) the interaction becomes the prevailing mechanism,
(b) the equations are very far from being solved explicitly,
(c) the problems can not be seen in any extent as perturbations of simpler (e.g. integrable) systems.
Ultimo aggiornamento: 23/07/2015 11:37
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