Calculus of Variations and Geometric Measure Theory

G. M. Coclite - N. De Nitti - A. Keimer

On a discontinuous nonlocal conservation law modeling material flow on conveyor belts

created by denitti on 20 Jul 2020


Submitted Paper

Inserted: 20 jul 2020
Last Updated: 20 jul 2020

Year: 2020


We prove existence of solutions to a conservation law with nonlocal discontinuous flux modeling material flow on a conveyor belt. The discontinuity is with respect to the unknown function and arises in a dynamic velocity field which is active only at high densities and takes into account the effect of colliding parts though the nonlocal operator. The strategy of the proof is based on the vanishing viscosity method. We smooth the discontinuity and add a second-order regularizing term. The key tools used to establish the convergence of the sequence of solutions of the approximating problems are a BV estimate ''away from the discontinuity'', a suitable application of Murat's compact embedding, and a diagonal argument.