“Scalar conservation laws with flux discontinuous in the conserved quantity: front-tracking and Hamilton-Jacobi approach”
Giovedì 3 Ottobre 2019, ore 13:30 - Aula 2AB45 - Maria Teresa Chiri (Università di Padova)
We examine a class of conservation laws with flux discontinuous in the conserved quantity that emerges in a model of industrial conveyor belt and in supply chains. We first introduce an appropriate notion of pair of entropic solution-flux, we provide existence of entropic solution-fluxes by front-tracking and we show a Kruzkhov’s type stability of such solutions. Next, we analyze the associated Hamilton-Jacobi equation, we derive an Hopf-Lax type representation formula of the solutions and we show how to recover the pair of entropic solution-flux of the conservation law from the gradient of the solution of the Hamilton-Jacobi equation. Finally, we consider the problem of a junction with a buffer (to store processed products) and with incoming and outgoing belts modeled by the class of conservation laws analyzed beforehand. Existence and uniqueness of the solution to the junction problem is established.