Selection of a Hele-Shaw Bubble via Exponential Asymptotics

The well-studied selection problems involving Saffman--Taylor fingers or Taylor--Saffman bubbles in a Hele-Shaw channel are prototypical examples of pattern selection. Exact solutions to the corresponding zero-surface-tension problems exist for an arbitrary finger or bubble speed, but the addition of surface tension leads to a discrete set of solution branches, all of which approach a single solution in the limit in which the surface tension...