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Hyperbolic-elliptic models for well-reservoir flow
Optimal control for continuous supply network models
1. | Technische Universität Kaiserslautern, Fachbereich Mathematik, Postfach 3049, D-67653 Kaiserslautern, Germany, Germany |
2. | Fraunhofer Institute ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany |
[1] |
Wen-Xiu Ma. Conservation laws by symmetries and adjoint symmetries. Discrete and Continuous Dynamical Systems - S, 2018, 11 (4) : 707-721. doi: 10.3934/dcdss.2018044 |
[2] |
Michael Herty, Veronika Sachers. Adjoint calculus for optimization of gas networks. Networks and Heterogeneous Media, 2007, 2 (4) : 733-750. doi: 10.3934/nhm.2007.2.733 |
[3] |
Mauro Garavello. A review of conservation laws on networks. Networks and Heterogeneous Media, 2010, 5 (3) : 565-581. doi: 10.3934/nhm.2010.5.565 |
[4] |
Georges Bastin, B. Haut, Jean-Michel Coron, Brigitte d'Andréa-Novel. Lyapunov stability analysis of networks of scalar conservation laws. Networks and Heterogeneous Media, 2007, 2 (4) : 751-759. doi: 10.3934/nhm.2007.2.751 |
[5] |
Martin Gugat, Alexander Keimer, Günter Leugering, Zhiqiang Wang. Analysis of a system of nonlocal conservation laws for multi-commodity flow on networks. Networks and Heterogeneous Media, 2015, 10 (4) : 749-785. doi: 10.3934/nhm.2015.10.749 |
[6] |
Markus Musch, Ulrik Skre Fjordholm, Nils Henrik Risebro. Well-posedness theory for nonlinear scalar conservation laws on networks. Networks and Heterogeneous Media, 2022, 17 (1) : 101-128. doi: 10.3934/nhm.2021025 |
[7] |
Rama Ayoub, Aziz Hamdouni, Dina Razafindralandy. A new Hodge operator in discrete exterior calculus. Application to fluid mechanics. Communications on Pure and Applied Analysis, 2021, 20 (6) : 2155-2185. doi: 10.3934/cpaa.2021062 |
[8] |
Avner Friedman. Conservation laws in mathematical biology. Discrete and Continuous Dynamical Systems, 2012, 32 (9) : 3081-3097. doi: 10.3934/dcds.2012.32.3081 |
[9] |
Len G. Margolin, Roy S. Baty. Conservation laws in discrete geometry. Journal of Geometric Mechanics, 2019, 11 (2) : 187-203. doi: 10.3934/jgm.2019010 |
[10] |
Mauro Garavello, Roberto Natalini, Benedetto Piccoli, Andrea Terracina. Conservation laws with discontinuous flux. Networks and Heterogeneous Media, 2007, 2 (1) : 159-179. doi: 10.3934/nhm.2007.2.159 |
[11] |
Ciro D'Apice, Rosanna Manzo. A fluid dynamic model for supply chains. Networks and Heterogeneous Media, 2006, 1 (3) : 379-398. doi: 10.3934/nhm.2006.1.379 |
[12] |
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 |
[13] |
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 |
[14] |
Stefano Bianchini, Elio Marconi. On the concentration of entropy for scalar conservation laws. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 73-88. doi: 10.3934/dcdss.2016.9.73 |
[15] |
Gabriella Bretti, Ciro D’Apice, Rosanna Manzo, Benedetto Piccoli. A continuum-discrete model for supply chains dynamics. Networks and Heterogeneous Media, 2007, 2 (4) : 661-694. doi: 10.3934/nhm.2007.2.661 |
[16] |
Christophe Prieur. Control of systems of conservation laws with boundary errors. Networks and Heterogeneous Media, 2009, 4 (2) : 393-407. doi: 10.3934/nhm.2009.4.393 |
[17] |
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 |
[18] |
Rinaldo M. Colombo, Kenneth H. Karlsen, Frédéric Lagoutière, Andrea Marson. Special issue on contemporary topics in conservation laws. Networks and Heterogeneous Media, 2016, 11 (2) : i-ii. doi: 10.3934/nhm.2016.11.2i |
[19] |
Boris Andreianov, Kenneth H. Karlsen, Nils H. Risebro. On vanishing viscosity approximation of conservation laws with discontinuous flux. Networks and Heterogeneous Media, 2010, 5 (3) : 617-633. doi: 10.3934/nhm.2010.5.617 |
[20] |
Laurent Lévi, Julien Jimenez. Coupling of scalar conservation laws in stratified porous media. Conference Publications, 2007, 2007 (Special) : 644-654. doi: 10.3934/proc.2007.2007.644 |
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