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The Evans function and stability criteria for degenerate viscous shock waves
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Traveling waves and shock waves
1. | Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, United States |
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[1] |
James K. Knowles. On shock waves in solids. Discrete and Continuous Dynamical Systems - B, 2007, 7 (3) : 573-580. doi: 10.3934/dcdsb.2007.7.573 |
[2] |
Yuri Gaididei, Anders Rønne Rasmussen, Peter Leth Christiansen, Mads Peter Sørensen. Oscillating nonlinear acoustic shock waves. Evolution Equations and Control Theory, 2016, 5 (3) : 367-381. doi: 10.3934/eect.2016009 |
[3] |
Frederike Kissling, Christian Rohde. The computation of nonclassical shock waves with a heterogeneous multiscale method. Networks and Heterogeneous Media, 2010, 5 (3) : 661-674. doi: 10.3934/nhm.2010.5.661 |
[4] |
Jonatan Lenells. Traveling waves in compressible elastic rods. Discrete and Continuous Dynamical Systems - B, 2006, 6 (1) : 151-167. doi: 10.3934/dcdsb.2006.6.151 |
[5] |
Peter Howard, K. Zumbrun. The Evans function and stability criteria for degenerate viscous shock waves. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 837-855. doi: 10.3934/dcds.2004.10.837 |
[6] |
Denis Serre, Alexis F. Vasseur. The relative entropy method for the stability of intermediate shock waves; the rich case. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4569-4577. doi: 10.3934/dcds.2016.36.4569 |
[7] |
Xiaojie Hou, Wei Feng. Traveling waves and their stability in a coupled reaction diffusion system. Communications on Pure and Applied Analysis, 2011, 10 (1) : 141-160. doi: 10.3934/cpaa.2011.10.141 |
[8] |
Tong Li, Jeungeun Park. Traveling waves in a chemotaxis model with logistic growth. Discrete and Continuous Dynamical Systems - B, 2019, 24 (12) : 6465-6480. doi: 10.3934/dcdsb.2019147 |
[9] |
Guangyu Zhao. Multidimensional periodic traveling waves in infinite cylinders. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 1025-1045. doi: 10.3934/dcds.2009.24.1025 |
[10] |
Matthew S. Mizuhara, Peng Zhang. Uniqueness and traveling waves in a cell motility model. Discrete and Continuous Dynamical Systems - B, 2019, 24 (6) : 2811-2835. doi: 10.3934/dcdsb.2018315 |
[11] |
Alejandro B. Aceves, Luis A. Cisneros-Ake, Antonmaria A. Minzoni. Asymptotics for supersonic traveling waves in the Morse lattice. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 975-994. doi: 10.3934/dcdss.2011.4.975 |
[12] |
Joseph Thirouin. Classification of traveling waves for a quadratic Szegő equation. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3099-3122. doi: 10.3934/dcds.2019128 |
[13] |
Johanna Ridder, Wen Shen. Traveling waves for nonlocal models of traffic flow. Discrete and Continuous Dynamical Systems, 2019, 39 (7) : 4001-4040. doi: 10.3934/dcds.2019161 |
[14] |
Thuc Manh Le, Nguyen Van Minh. Monotone traveling waves in a general discrete model for populations. Discrete and Continuous Dynamical Systems - B, 2017, 22 (8) : 3221-3234. doi: 10.3934/dcdsb.2017171 |
[15] |
Chuncheng Wang, Rongsong Liu, Junping Shi, Carlos Martinez del Rio. Traveling waves of a mutualistic model of mistletoes and birds. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 1743-1765. doi: 10.3934/dcds.2015.35.1743 |
[16] |
Zhaosheng Feng. Traveling waves to a reaction-diffusion equation. Conference Publications, 2007, 2007 (Special) : 382-390. doi: 10.3934/proc.2007.2007.382 |
[17] |
Zhiting Xu. Traveling waves for a diffusive SEIR epidemic model. Communications on Pure and Applied Analysis, 2016, 15 (3) : 871-892. doi: 10.3934/cpaa.2016.15.871 |
[18] |
Judith R. Miller, Huihui Zeng. Multidimensional stability of planar traveling waves for an integrodifference model. Discrete and Continuous Dynamical Systems - B, 2013, 18 (3) : 741-751. doi: 10.3934/dcdsb.2013.18.741 |
[19] |
Zhi-An Wang. Mathematics of traveling waves in chemotaxis --Review paper--. Discrete and Continuous Dynamical Systems - B, 2013, 18 (3) : 601-641. doi: 10.3934/dcdsb.2013.18.601 |
[20] |
Adèle Bourgeois, Victor LeBlanc, Frithjof Lutscher. Dynamical stabilization and traveling waves in integrodifference equations. Discrete and Continuous Dynamical Systems - S, 2020, 13 (11) : 3029-3045. doi: 10.3934/dcdss.2020117 |
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