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Details of Grant 

EPSRC Reference: EP/T021535/1
Title: PDEs and dynamical systems
Principal Investigator: Robinson, Professor JC
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematics
Organisation: University of Warwick
Scheme: Overseas Travel Grants (OTGS)
Starts: 01 April 2020 Ends: 31 March 2022 Value (£): 13,737
EPSRC Research Topic Classifications:
Mathematical Analysis Non-linear Systems Mathematics
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
25 Feb 2020 EPSRC Mathematical Sciences Prioritisation Panel February 2020 Announced
Summary on Grant Application Form
The grant is designed to support continued collaboration in various topics in partial differential equations (PDEs) and, more generally, dynamical systems.

PDEs provide one (very large) class of predictive models used throughout the sciences, and their mathematical study is well established. The study of the collection of all solutions of such a mathematical model, and the description of their behaviour, is the remit of the theory of dynamical systems.

This proposal investigates some fundamental models, e.g. the heat equation and the Navier-Stokes equations that model fluids, and aims to understand how the structure of the initial heat field can produce seemingly nonlinear behaviour in a linear system, and how numerical computations can be realted to an abstract mathematical treatment (in the case of the Navier-Stokes equations).

In the more abstract setting of dynamical systems, one strand will develop an appropriate framework in which to treat situations where the system itself (and not just its state) can change over time (so-called "non-autonomomus" dynamical systems).

Two more purely mathematical problems - both of which have applications (one in dynamical systems, one in PDEs) - seek to reproduce "finite-dimensional sets" using a finite collection of variables, and to approximate irregular functions by regular functions with "nice" properties.

As such the proposed topics cover a number of mathematical areas with - potentially - a large number of applications.
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Organisation Website: http://www.warwick.ac.uk