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.
On the pure side, topics include:
- Ergodic theory
- Functional and fractal analysis
- The rigorous analysis of ordinary and partial differential equations.
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.
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.
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.