Symmetry analysis of an equation for constrained optimal transport, modelling the distribution of ants round a nest

摘要

A second-order nonlinear partial differential equation modelling the optimal transport of food into an ant nest is derived. The Lie group method is used to determine group invariant solutions admitted by the model equation. Two classes of solutions are obtained. In the first case we are able to impose zero ant density on a circle which yields physically relevant solutions. Here, the optimal transport of food into the ant nest occurs when the foraging region has a circular boundary. In the second case we are only able to impose zero ant density at a point.