Conservation law models for supply chains

Applied Analysis Seminar

Meeting Details

For more information about this meeting, contact Kristin Berrigan, Mark Levi, Alexei Novikov, Mykhailo Potomkin, Leonid Berlyand.

Speaker: Fabio Ancona, University of Padova, Italy

Abstract: We introduce a new model for supply chains on a network based on conservation laws with discontinuous flux evolving on each arc (sub-chain) and on buffers of limited capacity in every junction (separating sub-chains). The dynamics of every arc is governed by a continuity equation describing the evolution of the density of objects processed by the supply chain. The flux is a discontinuous function of the density at the point of maximal density since at the maximal density it admits different values according with the free or congested status of the supply chain. We provide a definition of viscosity solution on each arc for the corresponding (discontinuous) Hamilton-Jacobi equation and we show that the space derivative of such solutions are entropy weak solutions of the conservation law that keep trace of the (free-congested) status transition in the point of discontinuity of the flux. Existence and uniqueness of solutions of the Hamilton-Jacobi equations and of the Cauchy problem for the corresponding conservation laws at the junction will be also discussed. This is a joint work with Maria Teresa Chiri (University of Padova)

Room Reservation Information

Room Number: 114 McAllister

Date: 04/24/2019

Time: 3:30pm - 4:30pm