Existence of Solutions for Supply Chain Models Based on Partial Differential Equations

Source abstract

We consider a model for supply chains governed by partial differential equations. The mathematical properties of a continuous model are discussed and existence and uniqueness are proven. Moreover, Lipschitz continuous dependence on the initial data is proven. We make use of the front tracking method to construct approximate solutions. The obtained results extend the preliminary work of [S. Göttlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545–559].