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Traveling waves and shock waves
The Evans function and stability criteria for degenerate viscous shock waves
1.  Department of Mathematics, Texas A&M University, College Station, TX 77845, United States 
2.  Mathematics Department, Indiana University, Bloomington, IN 47405, United States 
[1] 
Ramon Plaza, K. Zumbrun. An Evans function approach to spectral stability of smallamplitude shock profiles. Discrete & Continuous Dynamical Systems, 2004, 10 (4) : 885924. doi: 10.3934/dcds.2004.10.885 
[2] 
Georges Bastin, B. Haut, JeanMichel Coron, Brigitte d'AndréaNovel. Lyapunov stability analysis of networks of scalar conservation laws. Networks & Heterogeneous Media, 2007, 2 (4) : 751759. doi: 10.3934/nhm.2007.2.751 
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Todd Kapitula, Björn Sandstede. Eigenvalues and resonances using the Evans function. Discrete & Continuous Dynamical Systems, 2004, 10 (4) : 857869. doi: 10.3934/dcds.2004.10.857 
[4] 
Yuri Latushkin, Alim Sukhtayev. The Evans function and the WeylTitchmarsh function. Discrete & Continuous Dynamical Systems  S, 2012, 5 (5) : 939970. doi: 10.3934/dcdss.2012.5.939 
[5] 
Maria Laura Delle Monache, Paola Goatin. Stability estimates for scalar conservation laws with moving flux constraints. Networks & Heterogeneous Media, 2017, 12 (2) : 245258. doi: 10.3934/nhm.2017010 
[6] 
Avner Friedman. Conservation laws in mathematical biology. Discrete & Continuous Dynamical Systems, 2012, 32 (9) : 30813097. doi: 10.3934/dcds.2012.32.3081 
[7] 
Mauro Garavello. A review of conservation laws on networks. Networks & Heterogeneous Media, 2010, 5 (3) : 565581. doi: 10.3934/nhm.2010.5.565 
[8] 
Len G. Margolin, Roy S. Baty. Conservation laws in discrete geometry. Journal of Geometric Mechanics, 2019, 11 (2) : 187203. doi: 10.3934/jgm.2019010 
[9] 
Mauro Garavello, Roberto Natalini, Benedetto Piccoli, Andrea Terracina. Conservation laws with discontinuous flux. Networks & Heterogeneous Media, 2007, 2 (1) : 159179. doi: 10.3934/nhm.2007.2.159 
[10] 
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 & Applied Analysis, 2019, 18 (2) : 931942. doi: 10.3934/cpaa.2019045 
[11] 
Shuichi Kawashima, Shinya Nishibata, Masataka Nishikawa. Asymptotic stability of stationary waves for twodimensional viscous conservation laws in half plane. Conference Publications, 2003, 2003 (Special) : 469476. doi: 10.3934/proc.2003.2003.469 
[12] 
Björn Sandstede, Arnd Scheel. Evans function and blowup methods in critical eigenvalue problems. Discrete & Continuous Dynamical Systems, 2004, 10 (4) : 941964. doi: 10.3934/dcds.2004.10.941 
[13] 
WenXiu Ma. Conservation laws by symmetries and adjoint symmetries. Discrete & Continuous Dynamical Systems  S, 2018, 11 (4) : 707721. doi: 10.3934/dcdss.2018044 
[14] 
TaiPing Liu, ShihHsien Yu. Hyperbolic conservation laws and dynamic systems. Discrete & Continuous Dynamical Systems, 2000, 6 (1) : 143145. doi: 10.3934/dcds.2000.6.143 
[15] 
Yanbo Hu, Wancheng Sheng. The Riemann problem of conservation laws in magnetogasdynamics. Communications on Pure & Applied Analysis, 2013, 12 (2) : 755769. doi: 10.3934/cpaa.2013.12.755 
[16] 
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 
[17] 
Christophe Prieur. Control of systems of conservation laws with boundary errors. Networks & Heterogeneous Media, 2009, 4 (2) : 393407. doi: 10.3934/nhm.2009.4.393 
[18] 
Alberto Bressan, Marta Lewicka. A uniqueness condition for hyperbolic systems of conservation laws. Discrete & Continuous Dynamical Systems, 2000, 6 (3) : 673682. doi: 10.3934/dcds.2000.6.673 
[19] 
Rinaldo M. Colombo, Kenneth H. Karlsen, Frédéric Lagoutière, Andrea Marson. Special issue on contemporary topics in conservation laws. Networks & Heterogeneous Media, 2016, 11 (2) : iii. doi: 10.3934/nhm.2016.11.2i 
[20] 
Boris Andreianov, Kenneth H. Karlsen, Nils H. Risebro. On vanishing viscosity approximation of conservation laws with discontinuous flux. Networks & Heterogeneous Media, 2010, 5 (3) : 617633. doi: 10.3934/nhm.2010.5.617 
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