Grant: Canada Research Chairs
The University of British Columbia
$200,000.00
Nonlinear Partial Differential Equations
EF 2023-24
Résumé
Tornadoes and hurricanes are two examples of singularities in nature. Like all atmospheric phenomena, they must comply with the laws of Physics, expressed in mathematical form by Partial Differential Equations. Mathematically, solutions to PDE's that display abrupt changes in level (``interfaces''), or tornado-like rotation (``vortices'') are called singularities, and the challenge of understanding the mechanisms of singularity formation is a hot current topic. A rich collection of innovative methods is required. Recently we have developed and applied ``gluing methods''to produce striking examples and answer long-open questions. In the years ahead, I propose to build a unified framework for these methods and use it to study singularity formation in a diverse range of problems arising from geometry, physics, biology, chemistry, and social interactions.
Programme
Canada Research Chairs
Bénéficiaire
Emplacement
British Columbia, Canada
Type de bénéficiaire
Academia
Type
Grant
Source
NSERC's Awards Data
Tel que publié
Application id
CRC-2019-00415
Name nom
Wei, Juncheng
Department département
Head Office
Organization id
2
Institution établissement
The University of British Columbia
Province en
British Columbia
Province fr
Colombie-Britannique
Country en
CANADA
Country fr
CANADA
Fiscal year exercice financier
2023
Competition year année de concours
2019
Award amount
200000
Program id
CRC
Program name en
Canada Research Chairs
Program name fr
Chaires de recherche du Canada
Group en
DISCOVERY RESEARCH
Group fr
RECHERCHE AXÉE SUR LA DÉCOUVERTE
Committee code
9998
Committee name en
Canada Research Chair Selection Committee
Committee name fr
Comité de sélection des Chaires de recherche du Canada
Area of application code
9999
Area of application group en
Not available
Area of application group fr
Non disponible
Area of application en
Not available
Area of application fr
Non disponible
Research subject code
10000
Research subject group en
The field of research available
Research subject group fr
The field of research available
Research subject en
Le domaine de recherche disponible
Research subject fr
Le domaine de recherche disponible
Field of research list codes
RDF10101;RDF10102
Field of research list names en
Pure mathematics;Applied mathematics
Field of research list names fr
Mathématiques pures;Mathématiques appliquées
Application title
Nonlinear Partial Differential Equations
Keyword
Singularity formations
nonlinear elliptic and parabolic equations
gluing methods
interface problems
De Giorgi's conjecture
blow-ups
vortex dynamics
Application summary
Tornadoes and hurricanes are two examples of singularities in nature. Like all atmospheric phenomena, they must comply with the laws of Physics, expressed in mathematical form by Partial Differential Equations. Mathematically, solutions to PDE's that display abrupt changes in level (``interfaces''), or tornado-like rotation (``vortices'') are called singularities, and the challenge of understanding the mechanisms of singularity formation is a hot current topic. A rich collection of innovative methods is required. Recently we have developed and applied ``gluing methods''to produce striking examples and answer long-open questions. In the years ahead, I propose to build a unified framework for these methods and use it to study singularity formation in a diverse range of problems arising from geometry, physics, biology, chemistry, and social interactions.
