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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-08-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| 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. |
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| ISSN: | 2191-950X |