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On the convergence of viscous approximations after shock interactions
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 & Continuous Dynamical Systems  A, 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 & Continuous Dynamical Systems  S, 2016, 9 (1) : 7388. doi: 10.3934/dcdss.2016.9.73 
[3] 
TaiPing Liu, ShihHsien Yu. Hyperbolic conservation laws and dynamic systems. Discrete & Continuous Dynamical Systems  A, 2000, 6 (1) : 143145. doi: 10.3934/dcds.2000.6.143 
[4] 
Alberto Bressan, Marta Lewicka. A uniqueness condition for hyperbolic systems of conservation laws. Discrete & Continuous Dynamical Systems  A, 2000, 6 (3) : 673682. doi: 10.3934/dcds.2000.6.673 
[5] 
GuiQiang Chen, Monica Torres. On the structure of solutions of nonlinear hyperbolic systems of conservation laws. Communications on Pure & Applied Analysis, 2011, 10 (4) : 10111036. doi: 10.3934/cpaa.2011.10.1011 
[6] 
Stefano Bianchini. A note on singular limits to hyperbolic systems of conservation laws. Communications on Pure & Applied Analysis, 2003, 2 (1) : 5164. doi: 10.3934/cpaa.2003.2.51 
[7] 
Xavier Litrico, Vincent Fromion, Gérard Scorletti. Robust feedforward boundary control of hyperbolic conservation laws. Networks & Heterogeneous Media, 2007, 2 (4) : 717731. doi: 10.3934/nhm.2007.2.717 
[8] 
Constantine M. Dafermos. A variational approach to the Riemann problem for hyperbolic conservation laws. Discrete & Continuous Dynamical Systems  A, 2009, 23 (1&2) : 185195. doi: 10.3934/dcds.2009.23.185 
[9] 
Fumioki Asakura, Andrea Corli. The path decomposition technique for systems of hyperbolic conservation laws. Discrete & Continuous Dynamical Systems  S, 2016, 9 (1) : 1532. doi: 10.3934/dcdss.2016.9.15 
[10] 
Evgeny Yu. Panov. On a condition of strong precompactness and the decay of periodic entropy solutions to scalar conservation laws. Networks & Heterogeneous Media, 2016, 11 (2) : 349367. doi: 10.3934/nhm.2016.11.349 
[11] 
YoungSam Kwon. On the wellposedness of entropy solutions for conservation laws with source terms. Discrete & Continuous Dynamical Systems  A, 2009, 25 (3) : 933949. doi: 10.3934/dcds.2009.25.933 
[12] 
Darko Mitrovic. New entropy conditions for scalar conservation laws with discontinuous flux. Discrete & Continuous Dynamical Systems  A, 2011, 30 (4) : 11911210. doi: 10.3934/dcds.2011.30.1191 
[13] 
Giuseppe Maria Coclite, Lorenzo di Ruvo, Jan Ernest, Siddhartha Mishra. Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes. Networks & Heterogeneous Media, 2013, 8 (4) : 969984. doi: 10.3934/nhm.2013.8.969 
[14] 
Mapundi K. Banda, Michael Herty. Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws. Mathematical Control & Related Fields, 2013, 3 (2) : 121142. doi: 10.3934/mcrf.2013.3.121 
[15] 
Stefano Bianchini. On the shift differentiability of the flow generated by a hyperbolic system of conservation laws. Discrete & Continuous Dynamical Systems  A, 2000, 6 (2) : 329350. doi: 10.3934/dcds.2000.6.329 
[16] 
Tatsien Li, Libin Wang. Global exact shock reconstruction for quasilinear hyperbolic systems of conservation laws. Discrete & Continuous Dynamical Systems  A, 2006, 15 (2) : 597609. doi: 10.3934/dcds.2006.15.597 
[17] 
Boris Andreianov, Mohamed Karimou Gazibo. Explicit formulation for the Dirichlet problem for parabolichyperbolic conservation laws. Networks & Heterogeneous Media, 2016, 11 (2) : 203222. doi: 10.3934/nhm.2016.11.203 
[18] 
Yu Zhang, Yanyan Zhang. Riemann problems for a class of coupled hyperbolic systems of conservation laws with a source term. Communications on Pure & Applied Analysis, 2019, 18 (3) : 15231545. doi: 10.3934/cpaa.2019073 
[19] 
Hermano Frid. Invariant regions under LaxFriedrichs scheme for multidimensional systems of conservation laws. Discrete & Continuous Dynamical Systems  A, 1995, 1 (4) : 585593. doi: 10.3934/dcds.1995.1.585 
[20] 
Hongyun Peng, Lizhi Ruan, Changjiang Zhu. Convergence rates of zero diffusion limit on large amplitude solution to a conservation laws arising in chemotaxis. Kinetic & Related Models, 2012, 5 (3) : 563581. doi: 10.3934/krm.2012.5.563 
2017 Impact Factor: 1.179
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