We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in one-space dimension and establish global existence of entropy weak solutions with concentration to the Cauchy problem for any BV initial data that has finite total mass confined in a bounded interval and initial density uniformly positive therein. In addition, under a suitable condition on the initial data, we show that entropy weak solutions with concentration admit time-asymptotic flocking.

BV SOLUTIONS FOR A HYDRODYNAMIC MODEL OF FLOCKING–TYPE WITH ALL-TO-ALL INTERACTION KERNEL

Amadori Debora
Membro del Collaboration Group
;
2022

Abstract

We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in one-space dimension and establish global existence of entropy weak solutions with concentration to the Cauchy problem for any BV initial data that has finite total mass confined in a bounded interval and initial density uniformly positive therein. In addition, under a suitable condition on the initial data, we show that entropy weak solutions with concentration admit time-asymptotic flocking.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/165432
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