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| In this talk, I will discuss kinetic representation of flocking systems, like Cucker-Smale model and Motsch-Tadmor model. Flocking and clustering behaviors are observed, where we prove that flocking is guaranteed with strong nonlocal interaction. It leads to an infinite time concentration in velocity variable. Such $\delta$-singularity brings difficulties in numerical implementation. We use a discontinuous Galerkin method to construct high order positive preserving scheme to solve kinetic flocking systems. In the case of flocking, a method based on a scaling argument of the velocity variable is also introduced to solve the system. |
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