ON A MACROSCOPIC LIMIT OF A KINETIC MODEL OF ALIGNMENT

In the present paper we study the macroscopic limits of a kinetic model for interacting entities (individuals, organisms, cells). The kinetic model is one-dimensional and the entities are characterized by their position and orientation (+/-) with swarming interaction controlled by a sensitivity parameter. The macroscopic limits of the model are considered for solutions close either to the diffusive (isotropic) or to the aligned (swarming) equilibrium states for various values of that parameter. In the former case the classical linear diffusion equation results whereas in the latter a traveling wave solution does both in the zeroth (Euler) and first (Navier-Stokes) order of approximation.