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Details of Grant 

EPSRC Reference: EP/K008404/1
Title: Nonlinear Nonlocal Aggregation-Diffusion Partial Differential Equations and Applications
Principal Investigator: Carrillo, Professor J
Other Investigators:
Researcher Co-Investigators:
Dr Y Huang
Project Partners:
Department: Mathematics
Organisation: Imperial College London
Scheme: Standard Research
Starts: 03 April 2013 Ends: 02 April 2016 Value (£): 411,398
EPSRC Research Topic Classifications:
Mathematical Analysis Numerical Analysis
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
18 Sep 2012 Mathematics Prioritisation Panel Meeting September 2012 Announced
Summary on Grant Application Form
This proposal will focus on the development of new mathematical

analysis tools and methods, design of suitable numerical schemes,

and numerical simulation in some selected new applications of the

field of nonlinear nonlocal diffusion and kinetic equations inside

the broad area of Partial Differential Equations (PDEs). Among the

numerous areas of applications, we will concentrate particularly

on some examples which can be identified, at the modelling stage,

as systems made out of a large number of "individuals" which show

a "collective behaviour" and how to obtain from them "averaged"

information. The behaviour of individuals can be typically

modelled via stochastic/deterministic ODEs from which one obtains

mesoscopic and/or macroscopic descriptions based on mean-field

type PDEs leading to kinetic and/or continuum model systems. The

interplay between the aggregation/interaction behaviour (nonlocal,

nonlinear), the transport phenomena, and the nonlinear diffusion,

is the main goal of analysis of this proposal.

The research to be developed is centered on developing tools to

understand the long time asymptotics, stability of patterns, and

functional inequalities related to these equations from the

applied analysis viewpoint. On the other hand, developing

numerical schemes to solve accurately these models will help

understanding these theoretical issues while giving information

for the proposed applications. This proposal is a focal point of

several mathematical subareas, the research topics need tools and

ideas ranging from differential geometry to mathematical analysis

using probability theory and passing through modeling and

numerical analysis. It also touches different core areas of

nowadays interest in Science and Technology such as agent-based

models in mathematical biology. The emphasis of the proposal is in

applied and numerical analysis from a Partial Differential

Equations perspective.

Key Findings
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Potential use in non-academic contexts
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Date Materialised
Sectors submitted by the Researcher
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Project URL:  
Further Information:  
Organisation Website: http://www.imperial.ac.uk