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The Pullback equation for degenerate forms
Shock formation and breaking in granular avalanches
1. | Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, United States, United States |
[1] |
Tatsien Li, Libin Wang. Global exact shock reconstruction for quasilinear hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 597-609. doi: 10.3934/dcds.2006.15.597 |
[2] |
K. T. Joseph, Manas R. Sahoo. Vanishing viscosity approach to a system of conservation laws admitting $\delta''$ waves. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2091-2118. doi: 10.3934/cpaa.2013.12.2091 |
[3] |
Wen Shen. Traveling waves for conservation laws with nonlocal flux for traffic flow on rough roads. Networks and Heterogeneous Media, 2019, 14 (4) : 709-732. doi: 10.3934/nhm.2019028 |
[4] |
K. A. Ariyawansa, Leonid Berlyand, Alexander Panchenko. A network model of geometrically constrained deformations of granular materials. Networks and Heterogeneous Media, 2008, 3 (1) : 125-148. doi: 10.3934/nhm.2008.3.125 |
[5] |
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 |
[6] |
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 |
[7] |
Avner Friedman. Conservation laws in mathematical biology. Discrete and Continuous Dynamical Systems, 2012, 32 (9) : 3081-3097. doi: 10.3934/dcds.2012.32.3081 |
[8] |
Mauro Garavello. A review of conservation laws on networks. Networks and Heterogeneous Media, 2010, 5 (3) : 565-581. doi: 10.3934/nhm.2010.5.565 |
[9] |
Len G. Margolin, Roy S. Baty. Conservation laws in discrete geometry. Journal of Geometric Mechanics, 2019, 11 (2) : 187-203. doi: 10.3934/jgm.2019010 |
[10] |
Mauro Garavello, Roberto Natalini, Benedetto Piccoli, Andrea Terracina. Conservation laws with discontinuous flux. Networks and Heterogeneous Media, 2007, 2 (1) : 159-179. doi: 10.3934/nhm.2007.2.159 |
[11] |
Tong Yang, Huijiang Zhao. Asymptotics toward strong rarefaction waves for $2\times 2$ systems of viscous conservation laws. Discrete and Continuous Dynamical Systems, 2005, 12 (2) : 251-282. doi: 10.3934/dcds.2005.12.251 |
[12] |
Shuichi Kawashima, Shinya Nishibata, Masataka Nishikawa. Asymptotic stability of stationary waves for two-dimensional viscous conservation laws in half plane. Conference Publications, 2003, 2003 (Special) : 469-476. doi: 10.3934/proc.2003.2003.469 |
[13] |
Paolo Paoletti. Acceleration waves in complex materials. Discrete and Continuous Dynamical Systems - B, 2012, 17 (2) : 637-659. doi: 10.3934/dcdsb.2012.17.637 |
[14] |
Haolei Wang, Lei Zhang. Energy minimization and preconditioning in the simulation of athermal granular materials in two dimensions. Electronic Research Archive, 2020, 28 (1) : 405-421. doi: 10.3934/era.2020023 |
[15] |
Jerry L. Bona, Thierry Colin, Colette Guillopé. Propagation of long-crested water waves. Ⅱ. Bore propagation. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 5543-5569. doi: 10.3934/dcds.2019244 |
[16] |
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 |
[17] |
Wen-Xiu Ma. Conservation laws by symmetries and adjoint symmetries. Discrete and Continuous Dynamical Systems - S, 2018, 11 (4) : 707-721. doi: 10.3934/dcdss.2018044 |
[18] |
Tai-Ping Liu, Shih-Hsien Yu. Hyperbolic conservation laws and dynamic systems. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 143-145. doi: 10.3934/dcds.2000.6.143 |
[19] |
Yanbo Hu, Wancheng Sheng. The Riemann problem of conservation laws in magnetogasdynamics. Communications on Pure and Applied Analysis, 2013, 12 (2) : 755-769. doi: 10.3934/cpaa.2013.12.755 |
[20] |
Stefano Bianchini, Elio Marconi. On the concentration of entropy for scalar conservation laws. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 73-88. doi: 10.3934/dcdss.2016.9.73 |
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