An Analysis of a 2x2 Keyfitz-Kranzer Type Balance System with Varying Generalized Chaplygin Gas
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916888717557760 |
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| author | Frew, Jack Keyser, Nigel Kim, Ethan Paddock, Griffin Toumbleston, Camden Wilson, Sara Tsikkou, Charis |
| author_facet | Frew, Jack Keyser, Nigel Kim, Ethan Paddock, Griffin Toumbleston, Camden Wilson, Sara Tsikkou, Charis |
| contents | We consider a system of two balance laws of Keyfitz-Kranzer type with varying generalized Chaplygin gas, which exhibits negative pressure and is a product of a function of time and the inverse of a power of the density. The Chaplygin gas is a fluid designed to accommodate measurements for the early universe and late-time universal expansion while obeying the pressure-density-time relation. We produce an explanation and description of the non-self-similar Riemann solutions, including the non-classical singular solutions. We also find that due to a direct dependence on time, a change in the regions allowing for combinations of classical and non-classical singular solutions occurs, therefore a Riemann solution can have different solutions over several time intervals. Our findings are confirmed numerically using the local Lax-Friederichs scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20869 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Analysis of a 2x2 Keyfitz-Kranzer Type Balance System with Varying Generalized Chaplygin Gas Frew, Jack Keyser, Nigel Kim, Ethan Paddock, Griffin Toumbleston, Camden Wilson, Sara Tsikkou, Charis Analysis of PDEs General Relativity and Quantum Cosmology Mathematical Physics 34A05, 35L45, 35L65, 35L67, 65M06, 85-10, 85A40 We consider a system of two balance laws of Keyfitz-Kranzer type with varying generalized Chaplygin gas, which exhibits negative pressure and is a product of a function of time and the inverse of a power of the density. The Chaplygin gas is a fluid designed to accommodate measurements for the early universe and late-time universal expansion while obeying the pressure-density-time relation. We produce an explanation and description of the non-self-similar Riemann solutions, including the non-classical singular solutions. We also find that due to a direct dependence on time, a change in the regions allowing for combinations of classical and non-classical singular solutions occurs, therefore a Riemann solution can have different solutions over several time intervals. Our findings are confirmed numerically using the local Lax-Friederichs scheme. |
| title | An Analysis of a 2x2 Keyfitz-Kranzer Type Balance System with Varying Generalized Chaplygin Gas |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology Mathematical Physics 34A05, 35L45, 35L65, 35L67, 65M06, 85-10, 85A40 |
| url | https://arxiv.org/abs/2407.20869 |