Fractional Laplacian Advanced Research: a dynamical system approach

Información del proyecto

FLARe

Identificador del acuerdo de subvención: 891212

DOI

10.3030/891212

Proyecto finalizado el 22 Octubre 2021

Fecha de la firma de la CE 15 Diciembre 2020

Fecha de inicio

Fecha de finalización

Financiado con arreglo a

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Coste total

€ 162 806,40

Aportación de la UE

€ 162 806,40

Coordinado por

TECHNISCHE UNIVERSITAET MUENCHEN
Germany

Objetivo

FLARe falls into the fields of fractional nonlinear spatio-temporal evolution equations, their dynamical analysis and bifurcation structure, from a theoretical and numerical point of view. The fractional Laplacian well describes nonlocal super diffusion phenomena which naturally appear in many applications in physics, biology and economy, characterized by long-range interactions. In the theory of nonlocal operators it constitutes the counterpart of the standard Laplacian in the classical theory of partial differential equations. Despite their differences, most of the relevant questions associated to the Laplacian have an equivalent for the fractional Laplacian. The novel challenge of FLARe is to also extend the analytical and numerical tools coming from a dynamical system approach for standard diffusion equations, to treat fractional diffusion equations (e.g. amplitude equations, continuation softwares etc.). This will be done thanks to an innovative interaction between the theoretical results on fractional operators, established theory on PDEs dynamics, stability and bifurcations, new and efficient discretization techniques and the continuation software pde2path. Taken together, they are going to constitute a solid methodology to investigate the dynamical properties of nonlinear fractional diffusion equations. These aspects also constitute the long term impact of the action: a well established link of three research fields, namely fractional diffusion theory, the dynamical system approach to PDEs and continuation software available for standard diffusion equation, which are not so well connected at the moment. The new link between different communities, the important results achieved during the action, the new capabilities of the continuation software, the supervisor expertise and clear guidance, the training and the outstanding research environment provided by the host institution are going to be the springboard for the researcher to a future career in academia.

Ámbito científico (EuroSciVoc)

• ciencias naturales › informática y ciencias de la información › software
• ciencias naturales › matemáticas › matemáticas aplicadas › sistemas dinámicos
• ciencias naturales › matemáticas › matemáticas puras › análisis matemático › ecuaciones diferenciales › ecuaciones diferenciales parciales

Palabras clave

• Fractional Laplacian
• bifurcations
• numerical continuation
• Lyapunov-Schmidt
• center manifold
• amplitude equations
• pde2path
• stability
• dynamics

Programa(s)

• H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions PROGRAMA PRINCIPAL
  
• H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
  

Tema(s)

• MSCA-IF-2019 - Individual Fellowships
  

Régimen de financiación

MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)

Convocatoria de propuestas

H2020-MSCA-IF-2019

Coordinador

TECHNISCHE UNIVERSITAET MUENCHEN

• Aportación neta de la UEn: € 162 806,40
• Dirección: Arcisstrasse 21 ; 80333 Muenchen ; Alemania
• Región: Bayern › Oberbayern › München, Kreisfreie Stadt
• Tipo de actividad: Higher or Secondary Education Establishments
• Coste total: € 162 806,40