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Monday, 15 September 2014 23:45

A discontinuous Galerkin method on kinetic flocking models

 

Changhui Tan

Mathematical Models and Methods in Applied Sciences, Volume 27, No 7, pp. 1199-1221 (2017).


Abstract

We study kinetic representations of flocking models. They arise from agent-based models for self-organized dynamics, such as Cucker–Smale [Emergent behaviors in flocks, IEEE Trans. Autom. Control. 52 (2007) 852–862] and Motsch–Tadmor [A new model for self-organized dynamics and its flocking behavior, J. Statist. Phys. 144 (2011) 923– 947] models. We first establish a well-posedness theory and large-time flocking behavior for the kinetic systems, which indicates a concentration in velocity variable in infinite time. We then apply a discontinuous Galerkin method to treat the asymptotic \(\delta\)-singularity, and construct high-order positive-preserving schemes to solve kinetic flocking systems.


   doi:10.1142/S0218202517400139
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