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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De Gruyter
2025-08-01
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| Series: | Advances in Nonlinear Analysis |
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| Online Access: | https://doi.org/10.1515/anona-2025-0098 |
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| author | Liu Xiaoli Guo Lihui Hu Yanbo |
| author_facet | Liu Xiaoli Guo Lihui Hu Yanbo |
| author_sort | Liu Xiaoli |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4f40409aa84541939bbb2cba8e6ca3ee |
| institution | Kabale University |
| issn | 2191-950X |
| language | English |
| publishDate | 2025-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj-art-4f40409aa84541939bbb2cba8e6ca3ee2025-08-20T04:03:17ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2025-08-0114189692010.1515/anona-2025-0098Singularity for the macroscopic production model with Chaplygin gasLiu Xiaoli0Guo Lihui1Hu Yanbo2College of Mathematics and System Science, Xinjiang University, Urumqi, 830017, PR ChinaCollege of Mathematics and System Science, Xinjiang University, Urumqi, 830017, PR ChinaDepartment of Mathematics, Zhejiang University of Science and Technology, Hangzhou, 310023, PR ChinaIn 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.https://doi.org/10.1515/anona-2025-0098macroscopic production modelchaplygin gassingularity formationcharacteristic decompositionnumerical simulation35l6535l67 |
| spellingShingle | Liu Xiaoli Guo Lihui Hu Yanbo Singularity for the macroscopic production model with Chaplygin gas Advances in Nonlinear Analysis macroscopic production model chaplygin gas singularity formation characteristic decomposition numerical simulation 35l65 35l67 |
| title | Singularity for the macroscopic production model with Chaplygin gas |
| title_full | Singularity for the macroscopic production model with Chaplygin gas |
| title_fullStr | Singularity for the macroscopic production model with Chaplygin gas |
| title_full_unstemmed | Singularity for the macroscopic production model with Chaplygin gas |
| title_short | Singularity for the macroscopic production model with Chaplygin gas |
| title_sort | singularity for the macroscopic production model with chaplygin gas |
| topic | macroscopic production model chaplygin gas singularity formation characteristic decomposition numerical simulation 35l65 35l67 |
| url | https://doi.org/10.1515/anona-2025-0098 |
| work_keys_str_mv | AT liuxiaoli singularityforthemacroscopicproductionmodelwithchaplygingas AT guolihui singularityforthemacroscopicproductionmodelwithchaplygingas AT huyanbo singularityforthemacroscopicproductionmodelwithchaplygingas |