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Dynamical Systems and Partial Differential Equations Group
The research in this area focuses on a range of topics in analysis ranging from the pure to the applied end.
Overview
Pure mathematics
On the pure side, topics include:
- Ergodic theory
- Functional and fractal analysis
- The rigorous analysis of ordinary and partial differential equations.
Applied mathematics
On the applied side methods are used to analyse partial differential equations (PDEs) in various contexts such as:
- Nonlinear elastostatics
- Pattern formation
- Dispersive wave equations
- Navier-Stokes equations
- Delay equations.
Analysis on unbounded domains is of particular interest.
Our research
A recent development involves the construction of solutions to the Schrödinger equation that describes the process of electron emission from a metal surface, a process of considerable technological importance in the design of flat displays.
Another dimension is the calculus of variations, a subject with a long history, which has developed fresh new directions in the twenty-first century. A typical example comes from nonlinear elasticity, where the cost of deforming an elastic solid is represented by an energy functional.
Research areas
The group's research interests include the following:
- Quasiconvexity, elasticity and the calculus of variations
- Interaction of patterns
- Qualitative analysis of dissipative partial differential equations
- Pinning, capture and release of fronts by localised inhomogeneities
- Positivity of solutions to dissipative fourth-order PDEs
- Hamiltonian systems with symmetry
- Time semi-discretizations of semilinear PDEs.
Our people
Academic staff
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Dr Michele Bartuccelli
Reader
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Dr Werner Bauer
Lecturer in Mathematics
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Dr Jonathan Bevan
Reader
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Dr Jonathan Deane
Senior Lecturer
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Professor Mark Roberts
Emeritus Professor
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Dr Polina Vytnova
Lecturer
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Professor Sergey Zelik
Programme Leader