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...

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Bibliographic Details
Main Authors: Liu Xiaoli, Guo Lihui, Hu Yanbo
Format: Article
Language:English
Published: De Gruyter 2025-08-01
Series:Advances in Nonlinear Analysis
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Online Access:https://doi.org/10.1515/anona-2025-0098
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Summary: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 C1{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.
ISSN:2191-950X