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October  2004, 10(4): i-ii. doi: 10.3934/dcds.2004.10.4i

Traveling waves and shock waves

Xiao-Biao Lin 1, and  Stephen Schecter 1,

1. 

Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, United States

Published  March 2004

Traveling waves and shock waves are physically important solutions of partial differential equations. Papers in this special issue address two aspects of the theory of traveling waves and shock waves: (1) the linearized stability of traveling waves and (2) the Dafermos regularization of a system of conservation laws.

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Citation: Xiao-Biao Lin, Stephen Schecter. Traveling waves and shock waves. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : i-ii. doi: 10.3934/dcds.2004.10.4i
[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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