Explore the words cloud of the MinSol-PDEs project. It provides you a very rough idea of what is the project "MinSol-PDEs" about.
The following table provides information about the project.
BCAM - BASQUE CENTER FOR APPLIED MATHEMATICS
|Coordinator Country||Spain [ES]|
|Total cost||160˙932 €|
|EC max contribution||160˙932 € (100%)|
1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
|Duration (year-month-day)||from 2019-12-01 to 2022-04-01|
Take a look of project's partnership.
|1||BCAM - BASQUE CENTER FOR APPLIED MATHEMATICS||ES (BILBAO)||coordinator||160˙932.00|
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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The information about "MINSOL-PDES" are provided by the European Opendata Portal: CORDIS opendata.
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