Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 111-120 |
| Number of pages | 10 |
| Journal | Applied Mathematics and Computation |
| Volume | 158 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 25 Oct 2004 |
| Externally published | Yes |
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics
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