MinSol-PDEs
Financiado
Minimal solutions to nonlinear systems of PDEs
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 qualita...
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.
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Duración del proyecto: 35 meses
Fecha Inicio: 2019-04-09
Fecha Fin: 2022-04-01
Fecha Fin: 2022-04-01
Línea de financiación: concedida
El organismo H2020 notifico la concesión del proyecto el día 2022-04-01
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
MSCA-IF-2018:
Individual Fellowships
Cerrada
hace 6 años
Presupuesto
El presupuesto total del proyecto asciende a
161K€
Líder del proyecto
BCAM - BASQUE CENTER FOR APPLIED MATHEMATICS
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
5M
Perfil tecnológico
TRL
4-5
5M