| Abstract: |
| In this talk, we present some results on the time-asymptotic flocking of weak solutions to
a hydrodynamic model of flocking-type with all-to-all interaction kernel, in one-space dimension.
An appropriate notion of entropy weak solutions with bounded support is given to capture the behavior of solutions to the Cauchy problem with any BV initial data that has finite total mass confined in a bounded interval and initial density uniformly positive therein.
We will discuss the long time behavior of these solutions, which are shown to experience flocking for large time:
their support is uniformly bounded in time, and the velocity converges to the mean value. The rate of convergence is exponential. The proof is based on the decay of positive waves and on cancellation properties between positive and negative waves. |
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