کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
838792 | 908369 | 2007 | 20 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: On an aggregation model with long and short range interactions On an aggregation model with long and short range interactions](/preview/png/838792.png)
In recent papers the authors had proposed a stochastic model for swarm aggregation, based on individuals subject to long range attraction and short range repulsion, in addition to a classical Brownian random dispersal. Under suitable laws of large numbers they showed that, for a large number of individuals, the evolution of the empirical distribution of the population can be expressed in terms of an approximating nonlinear degenerate and nonlocal parabolic equation, which describes the limit.In this paper the well-posedness of such evolution equation is investigated, which invokes a notion of entropy solutions extended to the nonlocal case. We motivate entropy solutions from the discrete particle system and use them to prove uniqueness. Moreover, we provide existence results and discuss some basic properties of solutions. Finally, we apply a Lagrangian numerical scheme to perform numerical simulations in spatial dimension one.
Journal: Nonlinear Analysis: Real World Applications - Volume 8, Issue 3, July 2007, Pages 939–958