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EP/K008404/1 - Nonlinear Nonlocal Aggregation-Diffusion Partial Differential Equations and Applications

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Professor J Carrillo EP/K008404/1 - Nonlinear Nonlocal Aggregation-Diffusion Partial Differential Equations and Applications

Principal Investigator - Dept of Mathematics, Imperial College London

Scheme

Standard Research

Research Areas

Mathematical Analysis Mathematical Analysis

Numerical Analysis Numerical Analysis

Start Date

04/2013

End Date

04/2016

Value

£411,398

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Grant Description

Summary and Description of the grant

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.

Structured Data / Microdata


Grant Event Details:
Name: Nonlinear Nonlocal Aggregation-Diffusion Partial Differential Equations and Applications - EP/K008404/1
Start Date: 2013-04-03T00:00:00+00:00
End Date: 2016-04-02T00:00:00+00:00

Organization: Imperial College London

Description: 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 ...