Objetivo 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 themathematical 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. Moreprecisely, 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 problemsrelated to linear and nonlinear eigenvalues Ámbito científico natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationsnatural sciencesphysical sciencesastronomyplanetary sciencescelestial mechanicsnatural sciencesphysical sciencescondensed matter physicsquantum gasesnatural sciencesmathematicsapplied mathematicsnatural sciencesphysical sciencescondensed matter physicsbose-einstein condensates Programa(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Tema(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Convocatoria de propuestas ERC-2013-ADG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-AG - ERC Advanced Grant Institución de acogida UNIVERSITA DEGLI STUDI DI TORINO Aportación de la UE € 1 346 145,00 Dirección VIA GIUSEPPE VERDI 8 10124 Torino Italia Ver en el mapa Región Nord-Ovest Piemonte Torino Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Giampiero Salomone (Dr.) Investigador principal Susanna Terracini (Prof.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo UNIVERSITA DEGLI STUDI DI TORINO Italia Aportación de la UE € 1 346 145,00 Dirección VIA GIUSEPPE VERDI 8 10124 Torino Ver en el mapa Región Nord-Ovest Piemonte Torino Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Giampiero Salomone (Dr.) Investigador principal Susanna Terracini (Prof.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos
