Partial differential equations

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.