Abstract
Despite their wide presence in various models in the study of collective
behaviors, explicit swarming patterns are difficult to obtain. In this
paper, special stationary solutions of the aggregation equation with power-law
kernels are constructed by inverting Fredholm integral operators or by employing
certain integral identities. These solutions are expected to be the global
energy stable equilibria and to characterize the generic behaviors of stationary
solutions for more general interactions.
behaviors, explicit swarming patterns are difficult to obtain. In this
paper, special stationary solutions of the aggregation equation with power-law
kernels are constructed by inverting Fredholm integral operators or by employing
certain integral identities. These solutions are expected to be the global
energy stable equilibria and to characterize the generic behaviors of stationary
solutions for more general interactions.
| Original language | English |
|---|---|
| Pages (from-to) | 171 - 192 |
| Number of pages | 22 |
| Journal | Kinetic and Related Models |
| Volume | 10 |
| Issue number | 1 |
| Early online date | 30 Nov 2016 |
| DOIs | |
| Publication status | Published - 1 Mar 2017 |