Descrizione del progetto DEENESFRITPL Soluzioni minimali per risolvere le equazioni differenziali parziali non lineari Finanziato dal programma di azioni Marie Skłodowska-Curie, il progetto MinSol-PDEs condurrà uno studio sistematico di soluzioni minimali per un’ampia classe di equazioni differenziali parziali non lineari. Parte della ricerca sarà orientata verso i problemi di transizione di fase descritti dall’equazione di Allen-Cahn. L’idea principale consiste nel ridurre l’equazione a un sistema hamiltoniano per costruire nuove classi di soluzioni minimali e comprendere le condizioni che implicano una riduzione variabile. Un’altra parte della ricerca si concentrerà sull’equazione di Painlevé, che svolge un ruolo cruciale in vari ambiti, quali matrici casuali, sistemi integrali e superconduttvità. L’obiettivo principale consiste nel classificare e indagare le soluzioni minimali per i sistemi di tipo Painlevé in dimensioni basse. Mostra l’obiettivo del progetto Nascondi l’obiettivo del progetto Obiettivo The aim of this proposal is to provide a systematic study of minimal solutions for a large class of nonlinear systems of PDE. Namely we will construct minimal solutions with predefined characteristics and investigate their qualitative properties, addressing the fundamental challenges that appear in the case of systems and which cannot be tackled with tools from the scalar case.The first part focuses on phase transition problems described by the Allen-Cahn system. This is a hot and difficult topic linking PDE with the theory of minimal surfaces. The main idea is to reduce the Allen-Cahn system to a Hamiltonian system in order to construct new classes of minimal solutions, and understand the conditions implying the reduction of variables (vector analog of the celebrated De Giorgi conjecture). In the second part, our focus is on the Painlevé equation which plays a crucial role in areas as diverse as random matrices, integrable systems, and superconductivity. The objective is to classify and investigate the minimal solutions of Painlevé-type systems in low dimensions. These have direct applications in the study of vortices in liquid crystals and Bose-Einstein condensates. The proposed approach connects the Painlevé equation with a singular problem, easier to study. The fellow has a strong research record on the Allen-Cahn system (a book + 6 papers), and has also worked on the Ginzburg-Landau model of liquid crystals. On the one hand, he will develop his own innovative approaches to the proposed problems, and transfer his expertise to the host. On the other hand, at BCAM and through a secondment, he will link his previous research on liquid crystals to other alternative models (for which the supervisor is a world-leading expert), and to the theory of Bose-Einstein condensates. He will also acquire new skills in simulation and computation. The achievement of this project will reinforce Fellow's reputation and support him in obtaining a strong academic position. Campo scientifico natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesphysical sciencescondensed matter physicsbose-einstein condensatesnatural sciencesphysical scienceselectromagnetism and electronicssuperconductivityengineering and technologymaterials engineeringliquid crystals Programma(i) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Argomento(i) MSCA-IF-2018 - Individual Fellowships Invito a presentare proposte H2020-MSCA-IF-2018 Vedi altri progetti per questo bando Meccanismo di finanziamento MSCA-IF-EF-ST - Standard EF Coordinatore BCAM - BASQUE CENTER FOR APPLIED MATHEMATICS Contribution nette de l'UE € 160 932,48 Indirizzo AL MAZARREDO 14 48009 Bilbao Spagna Mostra sulla mappa Regione Noreste País Vasco Bizkaia Tipo di attività Research Organisations Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 160 932,48
