-
Previous Article
Perfect derivatives, conservative differences and entropy stable computation of hyperbolic conservation laws
- DCDS Home
- This Issue
-
Next Article
A drift-diffusion model for molecular motor transport in anisotropic filament bundles
The relative entropy method for the stability of intermediate shock waves; the rich case
1. | UMPA, ENS-Lyon 46, allée d'Italie 69364 LYON Cedex 07, France |
2. | Department of Mathematics, University of Texas at Austin, 1 University Station – C1200, Austin, TX 78712-0257, United States |
References:
[1] |
S. Benzoni-Gavage, D. Serre and K. Zumbrun, Alternate Evans functions and viscous shock waves, SIAM J. Math. Anal., 32 (2001), 929-962.
doi: 10.1137/S0036141099361834. |
[2] |
M.-J. Kang and A. Vasseur, Criteria on contractions for entropic discontinuities of systems of conservation laws, reprint, arXiv:1505.02245 (2015). |
[3] |
P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math., 10 (1957), 537-566.
doi: 10.1002/cpa.3160100406. |
[4] |
N. Leger, $L^2$-stability estimates for shock solutions of scalar conservation laws using the relative entropy method, Arch. Rational Mech. Anal., 199 (2011), 761-778.
doi: 10.1007/s00205-010-0341-7. |
[5] |
N. Leger and A. Vasseur, Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non-BV perturbations, Arch. Ration. Mech. Anal., 201 (2011), 271-302.
doi: 10.1007/s00205-011-0431-1. |
[6] |
T.-P. Liu, Pointwise convergence to $N$-waves for solutions of hyperbolic conservation laws, Bull. Inst. Math. Acad. Sinica, 15 (1987), 1-17. |
[7] |
A. Majda, The stability of multidimensional shock fronts, Memoirs Amer. Math. Soc., 41 (1983), iv+95 pp.
doi: 10.1090/memo/0275. |
[8] |
A. Majda, The existence of multidimensional shock fronts, Memoirs Amer. Math. Soc., 43 (1983), v+93 pp.
doi: 10.1090/memo/0281. |
[9] |
D. Serre, Richness and the classification of quasilinear hyperbolic systems. Multidimensional hyperbolic problems and computations (Minneapolis, MN, 1989), IMA Vol. Math. Appl., 29, Springer, New York, (1991), 315-333.
doi: 10.1007/978-1-4613-9121-0_24. |
[10] |
D. Serre, Systems of Conservation Laws, II, Cambridge Univ. Press, 2000. |
[11] |
D. Serre, The structure of dissipative viscous system of conservation laws, PhysicaD, 239 (2010), 1381-1386.
doi: 10.1016/j.physd.2009.03.014. |
[12] |
D. Serre, Long-time stability in systems of conservation laws, using relative entropy/energy, Arch. Ration. Mech. Anal., 219 (2016), 679-699.
doi: 10.1007/s00205-015-0903-9. |
[13] |
D. Serre, A. Vasseur, $L^2$-type contraction for systems of conservation laws, Journal de l'École polytechnique; Mathématiques, 1 (2014), 1-28.
doi: 10.5802/jep.1. |
show all references
References:
[1] |
S. Benzoni-Gavage, D. Serre and K. Zumbrun, Alternate Evans functions and viscous shock waves, SIAM J. Math. Anal., 32 (2001), 929-962.
doi: 10.1137/S0036141099361834. |
[2] |
M.-J. Kang and A. Vasseur, Criteria on contractions for entropic discontinuities of systems of conservation laws, reprint, arXiv:1505.02245 (2015). |
[3] |
P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math., 10 (1957), 537-566.
doi: 10.1002/cpa.3160100406. |
[4] |
N. Leger, $L^2$-stability estimates for shock solutions of scalar conservation laws using the relative entropy method, Arch. Rational Mech. Anal., 199 (2011), 761-778.
doi: 10.1007/s00205-010-0341-7. |
[5] |
N. Leger and A. Vasseur, Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non-BV perturbations, Arch. Ration. Mech. Anal., 201 (2011), 271-302.
doi: 10.1007/s00205-011-0431-1. |
[6] |
T.-P. Liu, Pointwise convergence to $N$-waves for solutions of hyperbolic conservation laws, Bull. Inst. Math. Acad. Sinica, 15 (1987), 1-17. |
[7] |
A. Majda, The stability of multidimensional shock fronts, Memoirs Amer. Math. Soc., 41 (1983), iv+95 pp.
doi: 10.1090/memo/0275. |
[8] |
A. Majda, The existence of multidimensional shock fronts, Memoirs Amer. Math. Soc., 43 (1983), v+93 pp.
doi: 10.1090/memo/0281. |
[9] |
D. Serre, Richness and the classification of quasilinear hyperbolic systems. Multidimensional hyperbolic problems and computations (Minneapolis, MN, 1989), IMA Vol. Math. Appl., 29, Springer, New York, (1991), 315-333.
doi: 10.1007/978-1-4613-9121-0_24. |
[10] |
D. Serre, Systems of Conservation Laws, II, Cambridge Univ. Press, 2000. |
[11] |
D. Serre, The structure of dissipative viscous system of conservation laws, PhysicaD, 239 (2010), 1381-1386.
doi: 10.1016/j.physd.2009.03.014. |
[12] |
D. Serre, Long-time stability in systems of conservation laws, using relative entropy/energy, Arch. Ration. Mech. Anal., 219 (2016), 679-699.
doi: 10.1007/s00205-015-0903-9. |
[13] |
D. Serre, A. Vasseur, $L^2$-type contraction for systems of conservation laws, Journal de l'École polytechnique; Mathématiques, 1 (2014), 1-28.
doi: 10.5802/jep.1. |
[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] |
Yue-Jun Peng, Yong-Fu Yang. Long-time behavior and stability of entropy solutions for linearly degenerate hyperbolic systems of rich type. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3683-3706. doi: 10.3934/dcds.2015.35.3683 |
[3] |
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 |
[4] |
Alberto Bressan, Marta Lewicka. A uniqueness condition for hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 673-682. doi: 10.3934/dcds.2000.6.673 |
[5] |
Gui-Qiang Chen, Monica Torres. On the structure of solutions of nonlinear hyperbolic systems of conservation laws. Communications on Pure and Applied Analysis, 2011, 10 (4) : 1011-1036. doi: 10.3934/cpaa.2011.10.1011 |
[6] |
Stefano Bianchini. A note on singular limits to hyperbolic systems of conservation laws. Communications on Pure and Applied Analysis, 2003, 2 (1) : 51-64. doi: 10.3934/cpaa.2003.2.51 |
[7] |
Fumioki Asakura, Andrea Corli. The path decomposition technique for systems of hyperbolic conservation laws. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 15-32. doi: 10.3934/dcdss.2016.9.15 |
[8] |
Eitan Tadmor. Perfect derivatives, conservative differences and entropy stable computation of hyperbolic conservation laws. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4579-4598. doi: 10.3934/dcds.2016.36.4579 |
[9] |
Mapundi K. Banda, Michael Herty. Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws. Mathematical Control and Related Fields, 2013, 3 (2) : 121-142. doi: 10.3934/mcrf.2013.3.121 |
[10] |
Yu Zhang, Yanyan Zhang. Riemann problems for a class of coupled hyperbolic systems of conservation laws with a source term. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1523-1545. doi: 10.3934/cpaa.2019073 |
[11] |
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 |
[12] |
Kenta Nakamura, Tohru Nakamura, Shuichi Kawashima. Asymptotic stability of rarefaction waves for a hyperbolic system of balance laws. Kinetic and Related Models, 2019, 12 (4) : 923-944. doi: 10.3934/krm.2019035 |
[13] |
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 and Applied Analysis, 2019, 18 (2) : 931-942. doi: 10.3934/cpaa.2019045 |
[14] |
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 |
[15] |
Xavier Litrico, Vincent Fromion, Gérard Scorletti. Robust feedforward boundary control of hyperbolic conservation laws. Networks and Heterogeneous Media, 2007, 2 (4) : 717-731. doi: 10.3934/nhm.2007.2.717 |
[16] |
Constantine M. Dafermos. A variational approach to the Riemann problem for hyperbolic conservation laws. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 185-195. doi: 10.3934/dcds.2009.23.185 |
[17] |
Weishi Liu. Multiple viscous wave fan profiles for Riemann solutions of hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 871-884. doi: 10.3934/dcds.2004.10.871 |
[18] |
Paolo Baiti, Helge Kristian Jenssen. Blowup in $\mathbf{L^{\infty}}$ for a class of genuinely nonlinear hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 837-853. doi: 10.3934/dcds.2001.7.837 |
[19] |
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 |
[20] |
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 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]