Existence of solution to supply chain models based on partial differential equation with discontinuous flux function

We consider a recently proposed model by Armbruster et al. (2011) [2] for supply chains with finite buffers. The continuous model is based on a scalar conservation law and discontinuous flux function. A suitable reformulation of the model is introduced and studied analytically. The latter include waves with infinite negative wave speed. Using wave-front tracking, existence of solutions is obtained for supply chains and sequences of supply chains. Numerical results are presented.