Exponential Asymptotics

Singularly perturbed differential equations generate divergent perturbation expansions, which can be shown to hide exponentially small terms "beyond all orders". These exponentials are responsible for selection phenomena in linear and nonlinear eigenvalue problems, with physical applications including Hele-Shaw flow, dendritic growth, vortex reconnection and gravity-capillary waves generated by submerged objects.

The great challenge at present is to extend recent results from one dimension to two-dimensional problems, allowing time-dependent problems to be considered.

People working in this area within OCIAM are

• Prof. Jon Chapman

• Dr John Ockendon