First-order aggregation models with alignment

PHYSICA D-NONLINEAR PHENOMENA

卷:325

Article

Fetecau, Razvan C.¹  Sun, Weiran¹  Tan, Changhui^2,3,4 

[1] Simon Fraser Univ, Dept Math, 8888 Univ Dr, Burnaby, BC V5A 1S6, Canada

[2] Univ Maryland, Dept Math, College Pk, MD 20705 USA

[3] Univ Maryland, CSCAMM, College Pk, MD 20705 USA

[4] Rice Univ, Dept Math, 6100 Main St, Houston, TX 77005 USA

关键词: Aggregation models;    Nonlocal interactions;    Kinetic equations;    Macroscopic limit;    Mass transport;    Particle methods;   

DOI  :  10.1016/j.physd.2016.03.011

来源: Elsevier

【 摘 要 】

We include alignment interactions in a well-studied first-order attractive repulsive macroscopic model for aggregation. The distinctive feature of the extended model is that the equation that specifies the velocity in terms of the population density, becomes implicit, and can have non-unique solutions. We investigate the well-posedness of the model and show rigorously how it can be obtained as a macroscopic limit of a second-order kinetic equation. We work within the space of probability measures with compact support and use mass transportation ideas and the characteristic method as essential tools in the analysis. A discretization procedure that parallels the analysis is formulated and implemented numerically in one and two dimensions. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free