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The convergence of the GRP scheme
1.  Institute of Mathematics, the Hebrew University of Jerusalem, 91904, Israel, Israel 
2.  School of Mathematical Sciences, Capital Normal University, 100037, Beijing 
[1] 
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 
[2] 
Stefano Bianchini, Elio Marconi. On the concentration of entropy for scalar conservation laws. Discrete and Continuous Dynamical Systems  S, 2016, 9 (1) : 7388. doi: 10.3934/dcdss.2016.9.73 
[3] 
Marco Di Francesco, Graziano Stivaletta. Convergence of the followtheleader scheme for scalar conservation laws with space dependent flux. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 233266. doi: 10.3934/dcds.2020010 
[4] 
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 
[5] 
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 
[6] 
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 
[7] 
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 
[8] 
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 
[9] 
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 
[10] 
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 
[11] 
Evgeny Yu. Panov. On a condition of strong precompactness and the decay of periodic entropy solutions to scalar conservation laws. Networks and Heterogeneous Media, 2016, 11 (2) : 349367. doi: 10.3934/nhm.2016.11.349 
[12] 
YoungSam Kwon. On the wellposedness of entropy solutions for conservation laws with source terms. Discrete and Continuous Dynamical Systems, 2009, 25 (3) : 933949. doi: 10.3934/dcds.2009.25.933 
[13] 
Darko Mitrovic. New entropy conditions for scalar conservation laws with discontinuous flux. Discrete and Continuous Dynamical Systems, 2011, 30 (4) : 11911210. doi: 10.3934/dcds.2011.30.1191 
[14] 
Giuseppe Maria Coclite, Lorenzo di Ruvo, Jan Ernest, Siddhartha Mishra. Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes. Networks and Heterogeneous Media, 2013, 8 (4) : 969984. doi: 10.3934/nhm.2013.8.969 
[15] 
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 
[16] 
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) : 329350. doi: 10.3934/dcds.2000.6.329 
[17] 
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 
[18] 
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 
[19] 
Boris Andreianov, Mohamed Karimou Gazibo. Explicit formulation for the Dirichlet problem for parabolichyperbolic conservation laws. Networks and Heterogeneous Media, 2016, 11 (2) : 203222. doi: 10.3934/nhm.2016.11.203 
[20] 
Hermano Frid. Invariant regions under LaxFriedrichs scheme for multidimensional systems of conservation laws. Discrete and Continuous Dynamical Systems, 1995, 1 (4) : 585593. doi: 10.3934/dcds.1995.1.585 
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