Centre for Analysis and Nonlinear Partial Differential Equations
Lead Research Organisation:
Heriot-Watt University
Department Name: S of Mathematical and Computer Sciences
Abstract
Nonlinear partial differential equations (PDE) are of universal applicability in the modelling of real-life situations from the flow of air around a wing to the behaviour of financial markets. They are also a natural language for describing the laws of mathematical physics and differential geometry. Their study poses profound intellectual challenges to pure mathematicians as well as important computational problems where accurate numerical data is required in specific applications. Despite its international importance and intense research activity on several fronts, including important breakthroughs in recent years, the UK appears to lag behind its competitors in this area.The present proposal is to establish the Centre for Analysis and Nonlinear Partial Differential Equations, run jointly by the University of Edinburgh and Heriot--Watt University at Edinburgh. This centre will improve the UK's current position through a number of specific actions:--- appointment of outstanding researchers in areas under-represented in the UK--- a programme of instructional workshops open to researchers in the UK and beyond--- two major research workshops on current trends and developments in nonlinear PDE--- a substantial visitor programme to bring the world's best researchers to the UK to give high-profile lectures and establish new research contacts--- development of new research links with industry and other interested parties--- development of new undergraduate and graduate courses in analysis aimed at meeting the needs of the next generation of researchersThe proposal comes from the Maxwell Institute of Mathematics, which is a new joint venture combining the strength of mathematical sciences at the University of Edinburgh and Heriot-Watt University. Funded by the Scottish Funding Council and the Office of Science and Technology, the Maxwell Institute aims to be a pre-eminent centre for research and post-graduate training in the mathematical sciences, offering an environment able to attract and foster the very best mathematical talent from around the world. The Maxwell Institute is one of five joint research initiatives, the others covering a wide range of topics in engineering and geoscience. The present bid will take advantage of the Maxwell Institute's position alongside the other joint research initiatives to develop new collaborations and applications of nonlinear PDE in these areas.The other distinctive feature of this proposal is the presence of the International Centre for Mathematical Sciences (ICMS) which is a joint initiative of the mathematicians at Edinburgh and Heriot-Watt which was set up in 1990. Since then ICMS has developed a reputation for the running of high-level international instructional and research workshops, and the infrastructure it provides will be crucial in organizing the proposed workshops. At the same time, these workshops provide a broadening of ICMS's current activities and will add to its international reputation.The new research grouping will be managed by a Scientific Steering Committee composed of two mathematicians from each of University of Edinburgh and Heriot-Watt University, and also including at least one representative from industry and at least one person from overseas. The committee will be regularly consulted, especially on the workshop and visitor programmes.
Publications
Boulton L
(2012)
On the Stability of a Forward-Backward Heat Equation
in Integral Equations and Operator Theory
Buckwar E
(2011)
An exact stochastic hybrid model of excitable membranes including spatio-temporal evolution.
in Journal of mathematical biology
Cheng C
(2008)
On the motion of vortex sheets with surface tension in three-dimensional Euler equations with vorticity
in Communications on Pure and Applied Mathematics
Cheng C
(2014)
Global existence and decay for solutions of the Hele-Shaw flow with injection
in Interfaces and Free Boundaries, Mathematical Analysis, Computation and Applications
Cheng C
(2010)
On the Limit as the Density Ratio Tends to Zero for Two Perfect Incompressible Fluids Separated by a Surface of Discontinuity
in Communications in Partial Differential Equations
Coutand D
(2012)
Well-Posedness in Smooth Function Spaces for the Moving-Boundary Three-Dimensional Compressible Euler Equations in Physical Vacuum
in Archive for Rational Mechanics and Analysis
Coutand D
(2013)
Well-Posedness of the Free-Boundary Compressible 3-D Euler Equations with Surface Tension and the Zero Surface Tension Limit
in SIAM Journal on Mathematical Analysis
Coutand D
(2013)
On the Finite-Time Splash and Splat Singularities for the 3-D Free-Surface Euler Equations
in Communications in Mathematical Physics
Coutand D
(2010)
Well-posedness in smooth function spaces for moving-boundary 1-D compressible euler equations in physical vacuum
in Communications on Pure and Applied Mathematics
Coutand D
(2010)
A Priori Estimates for the Free-Boundary 3D Compressible Euler Equations in Physical Vacuum
in Communications in Mathematical Physics
Eliasson H
(2008)
On Reducibility of Schrödinger Equations with Quasiperiodic in Time Potentials
in Communications in Mathematical Physics
Kuksin S
(2008)
On Distribution of Energy and Vorticity for Solutions of 2D Navier-Stokes Equation with Small Viscosity
in Communications in Mathematical Physics
Michalowski N
(2010)
Weighted norm inequalities for pseudo-pseudodifferential operators defined by amplitudes
in Journal of Functional Analysis
Michalowski N
(2018)
Weighted L p Boundedness of Pseudodifferential Operators and Applications
in Canadian Mathematical Bulletin
Paicu M
(2012)
Regularity of the global attractor and finite-dimensional behavior for the second grade fluid equations
in Journal of Differential Equations
Riedler M
(2013)
Almost sure convergence of numerical approximations for Piecewise Deterministic Markov Processes
in Journal of Computational and Applied Mathematics
Riedler M
(2012)
Limit theorems for infinite-dimensional piecewise deterministic Markov processes. Applications to stochastic excitable membrane models
in Electronic Journal of Probability
Description | This was a wide-ranging project to build capacity in the area of analysis and nonlinear partial differential equations, which was found to be in danger of getting dangerously small in numbers of active researchers. We built capacity by appointing people during the project and have continued to hire new staff in the area. More recently we have been awarded a CDT grant to train about 60 new PhD students in this area over the next 8 years, and we continue to deliver this goal. |
Exploitation Route | There were many technical results published in the academic literature which are attracting citations, and so are proving to be useful for others. |
Sectors | Aerospace Defence and Marine Electronics Energy Environment Financial Services and Management Consultancy Manufacturing including Industrial Biotechology |
Description | The findings are mainly in underlying science, and so support further developments in areas that are more directly applied. e.g. a conference was organised to bring together meteorologists and mathematical analysts. |
First Year Of Impact | 2007 |
Sector | Aerospace, Defence and Marine,Energy,Environment,Pharmaceuticals and Medical Biotechnology |
Impact Types | Societal Economic |
Description | EPSRC CDT |
Amount | £4,543,507 (GBP) |
Funding ID | EP/L016508/1 |
Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
Sector | Public |
Country | United Kingdom |
Start | 04/2014 |
End | 10/2022 |
Description | EPSRC Grant |
Amount | £255,619 (GBP) |
Funding ID | EP/H030514/1 |
Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
Sector | Public |
Country | United Kingdom |
Start | 07/2010 |
End | 07/2013 |
Description | EPSRC first grant scheme |
Amount | £101,427 (GBP) |
Funding ID | EP/I00761X/1 |
Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
Sector | Public |
Country | United Kingdom |
Start | 02/2011 |
End | 06/2013 |
Description | EPSRC first grant scheme |
Amount | £98,013 (GBP) |
Funding ID | EP/H051368/1 |
Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
Sector | Public |
Country | United Kingdom |
Start | 09/2010 |
End | 09/2011 |