Objectif
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
Champ scientifique
- natural sciencesmathematicspure mathematicsmathematical analysisdifferential equations
- natural sciencesphysical sciencesastronomyplanetary sciencescelestial mechanics
- natural sciencesphysical sciencescondensed matter physicsquantum gases
- natural sciencesmathematicsapplied mathematics
- natural sciencesphysical sciencescondensed matter physicsbose-einstein condensates
Appel à propositions
ERC-2013-ADG
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Régime de financement
ERC-AG - ERC Advanced GrantInstitution d’accueil
10124 Torino
Italie