Singularity for the macroscopic production model with Chaplygin gas

In this article, we investigate the formation of singularities in solutions of homogeneous and inhomogeneous systems for a macroscopic production model with Chaplygin gas using the method of characteristic decomposition. It is a model originating from production planning in supply chains. Since the model with the Chaplygin gas equation of state is a strictly hyperbolic system with both linearly degenerate characteristic field and genuinely nonlinear characteristic field, we can simultaneously study the blow-up of the solution itself and the blow-up of the derivative of the solution, in which the blow-up of the solution itself corresponds to the bottlenecks in the supply chains. Besides, we obtain the C 1 {C}^{1} estimates of the solution before the solution itself blows up. In addition, we give some representative examples of numerical simulations concerning the generation of singularities of solutions.

Abstract licence: CC BY

34 more references, whose wording the paper’s licence keeps private.

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.