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Comparison among different notions of solution for the $p$-system at a junction
1. | Dipartimento di Matematica, Via Branze, 38 – 25123 Brescia, Italy |
2. | Dipartimento di Scienze e Tecnologie Avanzate, Università del Piemonte Orientale “A. Avogadro”, Via Bellini 25/G, 15100 Alessandria |
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Constantine M. Dafermos. A variational approach to the Riemann problem for hyperbolic conservation laws. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 185-195. doi: 10.3934/dcds.2009.23.185 |
[2] |
Yu Zhang, Yanyan Zhang. Riemann problems for a class of coupled hyperbolic systems of conservation laws with a source term. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1523-1545. doi: 10.3934/cpaa.2019073 |
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Yanbo Hu, Wancheng Sheng. The Riemann problem of conservation laws in magnetogasdynamics. Communications on Pure and Applied Analysis, 2013, 12 (2) : 755-769. doi: 10.3934/cpaa.2013.12.755 |
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João-Paulo Dias, Mário Figueira. On the Riemann problem for some discontinuous systems of conservation laws describing phase transitions. Communications on Pure and Applied Analysis, 2004, 3 (1) : 53-58. doi: 10.3934/cpaa.2004.3.53 |
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Anupam Sen, T. Raja Sekhar. Structural stability of the Riemann solution for a strictly hyperbolic system of conservation laws with flux approximation. Communications on Pure and Applied Analysis, 2019, 18 (2) : 931-942. doi: 10.3934/cpaa.2019045 |
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Weishi Liu. Multiple viscous wave fan profiles for Riemann solutions of hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 871-884. doi: 10.3934/dcds.2004.10.871 |
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Tai-Ping Liu, Shih-Hsien Yu. Hyperbolic conservation laws and dynamic systems. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 143-145. doi: 10.3934/dcds.2000.6.143 |
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Zhi-Qiang Shao. Lifespan of classical discontinuous solutions to the generalized nonlinear initial-boundary Riemann problem for hyperbolic conservation laws with small BV data: shocks and contact discontinuities. Communications on Pure and Applied Analysis, 2015, 14 (3) : 759-792. doi: 10.3934/cpaa.2015.14.759 |
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Alberto Bressan, Marta Lewicka. A uniqueness condition for hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 673-682. doi: 10.3934/dcds.2000.6.673 |
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Gui-Qiang Chen, Monica Torres. On the structure of solutions of nonlinear hyperbolic systems of conservation laws. Communications on Pure and Applied Analysis, 2011, 10 (4) : 1011-1036. doi: 10.3934/cpaa.2011.10.1011 |
[11] |
Stefano Bianchini. A note on singular limits to hyperbolic systems of conservation laws. Communications on Pure and Applied Analysis, 2003, 2 (1) : 51-64. doi: 10.3934/cpaa.2003.2.51 |
[12] |
Fumioki Asakura, Andrea Corli. The path decomposition technique for systems of hyperbolic conservation laws. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 15-32. doi: 10.3934/dcdss.2016.9.15 |
[13] |
Neng Zhu, Zhengrong Liu, Fang Wang, Kun Zhao. Asymptotic dynamics of a system of conservation laws from chemotaxis. Discrete and Continuous Dynamical Systems, 2021, 41 (2) : 813-847. doi: 10.3934/dcds.2020301 |
[14] |
Rinaldo M. Colombo, Mauro Garavello. A Well Posed Riemann Problem for the $p$--System at a Junction. Networks and Heterogeneous Media, 2006, 1 (3) : 495-511. doi: 10.3934/nhm.2006.1.495 |
[15] |
Lihui Guo, Wancheng Sheng, Tong Zhang. The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system$^*$. Communications on Pure and Applied Analysis, 2010, 9 (2) : 431-458. doi: 10.3934/cpaa.2010.9.431 |
[16] |
Boris Andreianov, Mohamed Karimou Gazibo. Explicit formulation for the Dirichlet problem for parabolic-hyperbolic conservation laws. Networks and Heterogeneous Media, 2016, 11 (2) : 203-222. doi: 10.3934/nhm.2016.11.203 |
[17] |
Stefano Bianchini. On the shift differentiability of the flow generated by a hyperbolic system of conservation laws. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 329-350. doi: 10.3934/dcds.2000.6.329 |
[18] |
Mapundi K. Banda, Michael Herty. Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws. Mathematical Control and Related Fields, 2013, 3 (2) : 121-142. doi: 10.3934/mcrf.2013.3.121 |
[19] |
Tatsien Li, Libin Wang. Global exact shock reconstruction for quasilinear hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 597-609. doi: 10.3934/dcds.2006.15.597 |
[20] |
Tong Li, Nitesh Mathur. Riemann problem for a non-strictly hyperbolic system in chemotaxis. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 2173-2187. doi: 10.3934/dcdsb.2021128 |
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