We invite applications for a PhD studentship at the Department of Mathematics, University of Sussex. The research will focus on numerical methods for higher-order nonlinear partial differential equations of gradient flow type.
This studentship is jointly funded by EPSRC and the School of Mathematical & Physical Science, University of Sussex.
The Project in detail: Evolution equations with an underlying gradient flow structure have since long been of special interest in analysis and mathematical physics. Apart from their relevance in applications, these equations are of great interest in mathematical analysis, since the behaviour of their solutions is typically much richer than that of the well-studied second order nonlinear diffusion processes. Despite many advances in the study of existence, regularity and long-time behaviour, fundamental questions on qualitative properties of the solutions to higher-order equations remain open.
When it comes to solve equations of gradient flow type numerically, efficient schemes that respect the equation’s special structure are of particular interest. We aim to continue our work in this field and derive novel numerical methods for higher-order nonlinear partial differential equations. We will analyse and implement the novel methods to solve higher-order partial differential equations with applications in mathematical imaging (e.g., image impairing and image denoising) and semiconductor device simulation (e.g. for fluid type models with quantum effects).
We hold collaborations with a number of UK and international experts in the area.
The project will be supervised by Dr Bertram DÃ¼ring ([email protected]).
A Research Training Support Grant will be made available for additional training, visits to conferences etc.
Award amount Â£13,726 tax-free maintenance bursary plus fees waived for 3.5 years.
Eligibility Due to funding only UK and EU residents are eligible.
UK residents are eligible for full awards, including fees and maintenance.
EU residents are eligible for awards covering fees only, but EU students who have studied in the UK for the previous three years may be eligible for a full award. For a precise statement of eligibility, please consult this EPSRC web page:
Applicants must have (or expect to receive) a first class honours degree or MSc in Mathematics (or equivalent qualifications). The ideal candidate will be experienced in numerical methods and analysis for partial differential equations.
How to Apply Apply through the Sussex on-line postgraduate application system:
In the Other Information/Funding Section state that you are applying for “The PhD studentship on Higher Order non-linear PDEs with Dr Bertram DÃ¼ring”.
Send an email to Dr Bertram DÃ¼ring ([email protected]) to confirm that you have applied on-line for this award.
Timetable The very latest date we can consider applications is 2nd September 2013. Early application is advised because the studentship will be awarded as soon as a suitable candidate is found.
The start date of the studentship is 19th September 2013.