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.


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