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Solutions with large total variation to nonconservative hyperbolic systems
1.  Dipartimento di Matematica, Via Branze, 38 – 25123 Brescia, Italy 
2.  Dip. di Matematica e Applicazioni, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy 
[1] 
TaiPing Liu, ShihHsien Yu. Hyperbolic conservation laws and dynamic systems. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 143145. doi: 10.3934/dcds.2000.6.143 
[2] 
Eitan Tadmor. Perfect derivatives, conservative differences and entropy stable computation of hyperbolic conservation laws. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 45794598. doi: 10.3934/dcds.2016.36.4579 
[3] 
Alberto Bressan, Marta Lewicka. A uniqueness condition for hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 673682. doi: 10.3934/dcds.2000.6.673 
[4] 
GuiQiang Chen, Monica Torres. On the structure of solutions of nonlinear hyperbolic systems of conservation laws. Communications on Pure and Applied Analysis, 2011, 10 (4) : 10111036. doi: 10.3934/cpaa.2011.10.1011 
[5] 
Stefano Bianchini. A note on singular limits to hyperbolic systems of conservation laws. Communications on Pure and Applied Analysis, 2003, 2 (1) : 5164. doi: 10.3934/cpaa.2003.2.51 
[6] 
Fumioki Asakura, Andrea Corli. The path decomposition technique for systems of hyperbolic conservation laws. Discrete and Continuous Dynamical Systems  S, 2016, 9 (1) : 1532. doi: 10.3934/dcdss.2016.9.15 
[7] 
Christophe Chalons, Paola Goatin, Nicolas Seguin. General constrained conservation laws. Application to pedestrian flow modeling. Networks and Heterogeneous Media, 2013, 8 (2) : 433463. doi: 10.3934/nhm.2013.8.433 
[8] 
Xuemei Li, Zaijiu Shang. On the existence of invariant tori in nonconservative dynamical systems with degeneracy and finite differentiability. Discrete and Continuous Dynamical Systems, 2019, 39 (7) : 42254257. doi: 10.3934/dcds.2019171 
[9] 
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) : 121142. doi: 10.3934/mcrf.2013.3.121 
[10] 
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) : 15231545. doi: 10.3934/cpaa.2019073 
[11] 
Tatsien Li, Libin Wang. Global exact shock reconstruction for quasilinear hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 597609. doi: 10.3934/dcds.2006.15.597 
[12] 
Yanning Li, Edward Canepa, Christian Claudel. Efficient robust control of first order scalar conservation laws using semianalytical solutions. Discrete and Continuous Dynamical Systems  S, 2014, 7 (3) : 525542. doi: 10.3934/dcdss.2014.7.525 
[13] 
Tatsien Li (Daqian Li). Global exact boundary controllability for first order quasilinear hyperbolic systems. Discrete and Continuous Dynamical Systems  B, 2010, 14 (4) : 14191432. doi: 10.3934/dcdsb.2010.14.1419 
[14] 
Kaili Zhuang, Tatsien Li, Bopeng Rao. Exact controllability for first order quasilinear hyperbolic systems with internal controls. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 11051124. doi: 10.3934/dcds.2016.36.1105 
[15] 
Xavier Litrico, Vincent Fromion, Gérard Scorletti. Robust feedforward boundary control of hyperbolic conservation laws. Networks and Heterogeneous Media, 2007, 2 (4) : 717731. doi: 10.3934/nhm.2007.2.717 
[16] 
Constantine M. Dafermos. A variational approach to the Riemann problem for hyperbolic conservation laws. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 185195. doi: 10.3934/dcds.2009.23.185 
[17] 
Weishi Liu. Multiple viscous wave fan profiles for Riemann solutions of hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 871884. doi: 10.3934/dcds.2004.10.871 
[18] 
Paolo Baiti, Helge Kristian Jenssen. Blowup in $\mathbf{L^{\infty}}$ for a class of genuinely nonlinear hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 837853. doi: 10.3934/dcds.2001.7.837 
[19] 
Steinar Evje, Huanyao Wen, Lei Yao. Global solutions to a onedimensional nonconservative twophase model. Discrete and Continuous Dynamical Systems, 2016, 36 (4) : 19271955. doi: 10.3934/dcds.2016.36.1927 
[20] 
Prasanta Kumar Barik, Ankik Kumar Giri. A note on massconserving solutions to the coagulationfragmentation equation by using nonconservative approximation. Kinetic and Related Models, 2018, 11 (5) : 11251138. doi: 10.3934/krm.2018043 
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