-
Previous Article
Spoofing cyber attack detection in probe-based traffic monitoring systems using mixed integer linear programming
- NHM Home
- This Issue
-
Next Article
Constructing set-valued fundamental diagrams from Jamiton solutions in second order traffic models
Qualitative analysis of some PDE models of traffic flow
1. | Department of Mathematics, University of Iowa, Iowa City, IA 52242 |
References:
[1] |
A. Aw and M. Rascle, Resurrection of "second order" models of traffic flow,, SIAM J. Appl. Math., 60 (2000), 916.
doi: 10.1137/S0036139997332099. |
[2] |
M. Bando, K. Hasebe, A. Nakayama, A. Shibata and Y. Sugiyama, Dynamical model of traffic congestion and numerical simulation,, Phys. Rev. E, 51 (1995), 1035. Google Scholar |
[3] |
N. Bellomo and C. Dogbe, On the modeling of traffic and crowds: A survey of models, speculations, and perspectives,, SIAM Rev., 53 (2011), 409.
doi: 10.1137/090746677. |
[4] |
N. Bellomo and V. Coscia, First order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow,, C. R. Mecanique, 333 (2005), 843.
doi: 10.1016/j.crme.2005.09.004. |
[5] |
F. Berthelin, P. Degond, M. Delitala and M. Rascle, A model for the formation and evolution of traffic jams,, Arch. Rational Mech. Anal., 187 (2008), 185.
doi: 10.1007/s00205-007-0061-9. |
[6] |
F. Berthelin, P. Degond, V. Le Blanc, S. Moutari, M. Rascle and J. Royer, A traffic-flow model with constraints for the modelling of traffic jams,, Math. Mod. Meth. Appl. Sci., 18 (2008), 1269.
doi: 10.1142/S0218202508003030. |
[7] |
V. Coscia, On a closure of mass conservation equation and stability analysis in the mathematical theory of vehicular traffic flow,, C. R. Mecanique, 332 (2004), 585.
doi: 10.1016/j.crme.2004.03.016. |
[8] |
C. Daganzo, Requiem for second-order approximations of traffic flow,, Transportation Research, 29 (1995), 277.
doi: 10.1016/0191-2615(95)00007-Z. |
[9] |
P. Degond and M. Delitala, Modelling and simulation of vehicular traffic jam formation,, Kinetic Related Models, 1 (2008), 279.
doi: 10.3934/krm.2008.1.279. |
[10] |
D. Helbing, Improved fluid-dynamic model for vehicular traffic,, Physical Review E, 51 (1995), 3154.
doi: 10.1103/PhysRevE.51.3164. |
[11] |
D. Helbing, Traffic and related self-driven many-particle systems,, Rev. Modern Phy., 73 (2001), 1067.
doi: 10.1103/RevModPhys.73.1067. |
[12] |
D. Helbing, Derivation of non-local macroscopic traffic equations and consistent traffic pressures from microscopic car-following models,, Eur. Phys. J. B, 69 (2009), 539. Google Scholar |
[13] |
S. Jin and Jian-Guo Liu, Relaxation and diffusion enhanced dispersive waves,, Proceedings: Mathematical and Physical Sciences, 446 (1994), 555. Google Scholar |
[14] |
W. L. Jin and H. M. Zhang, The formation and structure of vehicle clusters in the Payne-Whitham traffic flow model,, Transportation Research, 37 (2003), 207.
doi: 10.1016/S0191-2615(02)00008-5. |
[15] |
B.S. Kerner and P. Konhäuser, Structure and parameters of clusters in traffic flow,, Physical Review E, 50 (1994), 54.
doi: 10.1103/PhysRevE.50.54. |
[16] |
A. Klar and R. Wegener, Kinetic derivation of macroscopic anticipation models for vehicular traffic,, SIAM J. Appl. Math., 60 (2000), 1749.
doi: 10.1137/S0036139999356181. |
[17] |
R. D. Kühne, Macroscopic freeway model for dense traffic-stop-start waves and incident detection,, Ninth International Symposium on Transportation and Traffic Theory, (1984), 21. Google Scholar |
[18] |
A. Kurganov and A. Polizzi, Non-oscillatory central schemes for traffic flow models with Arrhenius look-ahead dynamics,, Netw. Heterog. Media, 4 (2009), 431.
doi: 10.3934/nhm.2009.4.431. |
[19] |
D. A. Kurtze and D. C. Hong, Traffic jams, granular flow, and soliton selection,, Phys. Rev. E, 52 (1995), 218.
doi: 10.1103/PhysRevE.52.218. |
[20] |
H. Y. Lee, H.-W. Lee and D. Kim, Steady-state solutions of hydrodynamic traffic models,, Phys. Rev. E, 69 (2004).
doi: 10.1103/PhysRevE.69.016118. |
[21] |
Dong Li and Tong Li, Shock formation in a traffic flow model with arrhenius look-ahead dynamics,, Networks and Heterogeneous Media, 6 (2011), 681.
doi: 10.3934/nhm.2011.6.681. |
[22] |
Tong Li, Global solutions and zero relaxation limit for a traffic flow model,, SIAM J. Appl. Math., 61 (2000), 1042.
doi: 10.1137/S0036139999356788. |
[23] |
Tong Li, $L^1$ stability of conservation laws for a traffic flow model,, Electron. J. Diff. Eqns., 2001 ().
|
[24] |
Tong Li, Well-posedness theory of an inhomogeneous traffic flow model,, Discrete and Continuous Dynamical Systems, 2 (2002), 401.
doi: 10.3934/dcdsb.2002.2.401. |
[25] |
Tong Li, Global solutions of nonconcave hyperbolic conservation laws with relaxation arising from traffic flow,, J. Diff. Eqns., 190 (2003), 131.
doi: 10.1016/S0022-0396(03)00014-7. |
[26] |
Tong Li, Mathematical modelling of traffic flows,, Hyperbolic problems: Theory, (2003), 695.
|
[27] |
Tong Li, Modelling traffic flow with a time-dependent fundamental diagram,, Math. Methods Appl. Sci., 27 (2004), 583.
doi: 10.1002/mma.470. |
[28] |
Tong Li, Nonlinear dynamics of traffic jams,, Physica D, 207 (2005), 41.
doi: 10.1016/j.physd.2005.05.011. |
[29] |
Tong Li, Instability and formation of clustering solutions of traffic flow,, Bulletin of the Institute of Mathematics, 2 (2007), 281.
|
[30] |
Tong Li, Stability of traveling waves in quasi-linear hyperbolic systems with relaxation and diffusion,, SIAM J. Math. Anal., 40 (2008), 1058.
doi: 10.1137/070690638. |
[31] |
Tong Li and Hailiang Liu, Stability of a traffic flow model with nonconvex relaxation,, Comm. Math. Sci., 3 (2005), 101.
|
[32] |
Tong Li and Hailiang Liu, Critical thresholds in hyperbolic relaxation systems,, J. Diff. Eqns., 247 (2009), 33.
doi: 10.1016/j.jde.2009.03.032. |
[33] |
Tong Li and Hailiang Liu, Critical thresholds in a relaxation system with resonance of characteristic speeds,, Discrete and Continuous Dynamical Systems - Series A, 24 (2009), 511.
doi: 10.3934/dcds.2009.24.511. |
[34] |
Tong Li and Hailiang Liu, Critical thresholds in a relaxation model for traffic flows,, Indiana Univ. Math. J., 57 (2008), 1409.
doi: 10.1512/iumj.2008.57.3215. |
[35] |
Tong Li and Yaping Wu, Linear and nonlinear exponential stability of traveling waves for hyperbolic systems with relaxation,, Comm. Math. Sci., 7 (2009), 571.
|
[36] |
Tong Li and H. M. Zhang, The mathematical theory of an enhanced nonequilibrium traffic flow model,, Network and Spatial Economics, 1&2 (2001), 167. Google Scholar |
[37] |
M. J. Lighthill and G. B. Whitham, On kinematic waves: II. A theory of traffic flow on long crowded roads,, Proc. Roy. Soc., A229 (1955), 317.
doi: 10.1098/rspa.1955.0089. |
[38] |
T. Nagatani, The physics of traffic jams,, Rep. Prog. Phys., 65 (2002), 1331.
doi: 10.1088/0034-4885/65/9/203. |
[39] |
K. Nagel, Particle hopping models and traffic flow theory,, Phys. Rev. E, 53 (1996), 4655. Google Scholar |
[40] |
O. A. Oleinik, Discontinuous solutions of non-linear differential equations,, (Russian) Uspehi. Mat. Nauk., 12 (1957), 3.
|
[41] |
H. J. Payne, Models of freeway traffic and control,, "Simulation Councils Proc. Ser. : Mathematical Models of Public Systems,", 1 (1971), 51. Google Scholar |
[42] |
I. Prigogine and R. Herman, "Kinetic Theory of Vehicular Traffic,", American Elsevier Publishing Company Inc., (1971). Google Scholar |
[43] |
P. I. Richards, Shock waves on highway,, Operations Research, 4 (1956), 42.
doi: 10.1287/opre.4.1.42. |
[44] |
A. Sopasakis and M. Katsoulakis, Stochastic modeling and simulation of traffic flow: Asymmetric single exclusion process with Arrhenius look-ahead dynamics,, SIAM J. Appl. Math., 66 (2006), 921.
doi: 10.1137/040617790. |
[45] |
Lina Wang, Yaping Wu and Tong Li, Exponential stability of large-amplitude traveling fronts for quasi-linear relaxation systems with diffusion,, Physica D, 240 (2011), 971.
doi: 10.1016/j.physd.2011.02.003. |
[46] |
G. B. Whitham, "Linear and Nonlinear Waves,", Pure and Applied Mathematics. Wiley-Interscience [John Wiley & Sons], (1974).
|
[47] |
Lei Yu, Tong Li and Zhong-Ke Shi, Density waves in a traffic flow model with reactive-time delay,, Physica A, 389 (2010), 2607.
doi: 10.1016/j.physa.2010.03.009. |
[48] |
Lei Yu, Tong Li and Zhong-Ke Shi, The effect of diffusion in a new viscous continuum model,, Physics Letters, 374 (2010), 2346.
doi: 10.1016/j.physleta.2010.03.056. |
[49] |
H. M. Zhang, A non-equilibrium traffic model devoid of gas-like behavior,, Transportation Research, 36 (2002), 275.
doi: 10.1016/S0191-2615(00)00050-3. |
[50] |
H. M. Zhang, Driver memory, traffic viscosity and a viscous vehicular traffic flow model,, Transportation Research, 37 (2003), 27. Google Scholar |
show all references
References:
[1] |
A. Aw and M. Rascle, Resurrection of "second order" models of traffic flow,, SIAM J. Appl. Math., 60 (2000), 916.
doi: 10.1137/S0036139997332099. |
[2] |
M. Bando, K. Hasebe, A. Nakayama, A. Shibata and Y. Sugiyama, Dynamical model of traffic congestion and numerical simulation,, Phys. Rev. E, 51 (1995), 1035. Google Scholar |
[3] |
N. Bellomo and C. Dogbe, On the modeling of traffic and crowds: A survey of models, speculations, and perspectives,, SIAM Rev., 53 (2011), 409.
doi: 10.1137/090746677. |
[4] |
N. Bellomo and V. Coscia, First order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow,, C. R. Mecanique, 333 (2005), 843.
doi: 10.1016/j.crme.2005.09.004. |
[5] |
F. Berthelin, P. Degond, M. Delitala and M. Rascle, A model for the formation and evolution of traffic jams,, Arch. Rational Mech. Anal., 187 (2008), 185.
doi: 10.1007/s00205-007-0061-9. |
[6] |
F. Berthelin, P. Degond, V. Le Blanc, S. Moutari, M. Rascle and J. Royer, A traffic-flow model with constraints for the modelling of traffic jams,, Math. Mod. Meth. Appl. Sci., 18 (2008), 1269.
doi: 10.1142/S0218202508003030. |
[7] |
V. Coscia, On a closure of mass conservation equation and stability analysis in the mathematical theory of vehicular traffic flow,, C. R. Mecanique, 332 (2004), 585.
doi: 10.1016/j.crme.2004.03.016. |
[8] |
C. Daganzo, Requiem for second-order approximations of traffic flow,, Transportation Research, 29 (1995), 277.
doi: 10.1016/0191-2615(95)00007-Z. |
[9] |
P. Degond and M. Delitala, Modelling and simulation of vehicular traffic jam formation,, Kinetic Related Models, 1 (2008), 279.
doi: 10.3934/krm.2008.1.279. |
[10] |
D. Helbing, Improved fluid-dynamic model for vehicular traffic,, Physical Review E, 51 (1995), 3154.
doi: 10.1103/PhysRevE.51.3164. |
[11] |
D. Helbing, Traffic and related self-driven many-particle systems,, Rev. Modern Phy., 73 (2001), 1067.
doi: 10.1103/RevModPhys.73.1067. |
[12] |
D. Helbing, Derivation of non-local macroscopic traffic equations and consistent traffic pressures from microscopic car-following models,, Eur. Phys. J. B, 69 (2009), 539. Google Scholar |
[13] |
S. Jin and Jian-Guo Liu, Relaxation and diffusion enhanced dispersive waves,, Proceedings: Mathematical and Physical Sciences, 446 (1994), 555. Google Scholar |
[14] |
W. L. Jin and H. M. Zhang, The formation and structure of vehicle clusters in the Payne-Whitham traffic flow model,, Transportation Research, 37 (2003), 207.
doi: 10.1016/S0191-2615(02)00008-5. |
[15] |
B.S. Kerner and P. Konhäuser, Structure and parameters of clusters in traffic flow,, Physical Review E, 50 (1994), 54.
doi: 10.1103/PhysRevE.50.54. |
[16] |
A. Klar and R. Wegener, Kinetic derivation of macroscopic anticipation models for vehicular traffic,, SIAM J. Appl. Math., 60 (2000), 1749.
doi: 10.1137/S0036139999356181. |
[17] |
R. D. Kühne, Macroscopic freeway model for dense traffic-stop-start waves and incident detection,, Ninth International Symposium on Transportation and Traffic Theory, (1984), 21. Google Scholar |
[18] |
A. Kurganov and A. Polizzi, Non-oscillatory central schemes for traffic flow models with Arrhenius look-ahead dynamics,, Netw. Heterog. Media, 4 (2009), 431.
doi: 10.3934/nhm.2009.4.431. |
[19] |
D. A. Kurtze and D. C. Hong, Traffic jams, granular flow, and soliton selection,, Phys. Rev. E, 52 (1995), 218.
doi: 10.1103/PhysRevE.52.218. |
[20] |
H. Y. Lee, H.-W. Lee and D. Kim, Steady-state solutions of hydrodynamic traffic models,, Phys. Rev. E, 69 (2004).
doi: 10.1103/PhysRevE.69.016118. |
[21] |
Dong Li and Tong Li, Shock formation in a traffic flow model with arrhenius look-ahead dynamics,, Networks and Heterogeneous Media, 6 (2011), 681.
doi: 10.3934/nhm.2011.6.681. |
[22] |
Tong Li, Global solutions and zero relaxation limit for a traffic flow model,, SIAM J. Appl. Math., 61 (2000), 1042.
doi: 10.1137/S0036139999356788. |
[23] |
Tong Li, $L^1$ stability of conservation laws for a traffic flow model,, Electron. J. Diff. Eqns., 2001 ().
|
[24] |
Tong Li, Well-posedness theory of an inhomogeneous traffic flow model,, Discrete and Continuous Dynamical Systems, 2 (2002), 401.
doi: 10.3934/dcdsb.2002.2.401. |
[25] |
Tong Li, Global solutions of nonconcave hyperbolic conservation laws with relaxation arising from traffic flow,, J. Diff. Eqns., 190 (2003), 131.
doi: 10.1016/S0022-0396(03)00014-7. |
[26] |
Tong Li, Mathematical modelling of traffic flows,, Hyperbolic problems: Theory, (2003), 695.
|
[27] |
Tong Li, Modelling traffic flow with a time-dependent fundamental diagram,, Math. Methods Appl. Sci., 27 (2004), 583.
doi: 10.1002/mma.470. |
[28] |
Tong Li, Nonlinear dynamics of traffic jams,, Physica D, 207 (2005), 41.
doi: 10.1016/j.physd.2005.05.011. |
[29] |
Tong Li, Instability and formation of clustering solutions of traffic flow,, Bulletin of the Institute of Mathematics, 2 (2007), 281.
|
[30] |
Tong Li, Stability of traveling waves in quasi-linear hyperbolic systems with relaxation and diffusion,, SIAM J. Math. Anal., 40 (2008), 1058.
doi: 10.1137/070690638. |
[31] |
Tong Li and Hailiang Liu, Stability of a traffic flow model with nonconvex relaxation,, Comm. Math. Sci., 3 (2005), 101.
|
[32] |
Tong Li and Hailiang Liu, Critical thresholds in hyperbolic relaxation systems,, J. Diff. Eqns., 247 (2009), 33.
doi: 10.1016/j.jde.2009.03.032. |
[33] |
Tong Li and Hailiang Liu, Critical thresholds in a relaxation system with resonance of characteristic speeds,, Discrete and Continuous Dynamical Systems - Series A, 24 (2009), 511.
doi: 10.3934/dcds.2009.24.511. |
[34] |
Tong Li and Hailiang Liu, Critical thresholds in a relaxation model for traffic flows,, Indiana Univ. Math. J., 57 (2008), 1409.
doi: 10.1512/iumj.2008.57.3215. |
[35] |
Tong Li and Yaping Wu, Linear and nonlinear exponential stability of traveling waves for hyperbolic systems with relaxation,, Comm. Math. Sci., 7 (2009), 571.
|
[36] |
Tong Li and H. M. Zhang, The mathematical theory of an enhanced nonequilibrium traffic flow model,, Network and Spatial Economics, 1&2 (2001), 167. Google Scholar |
[37] |
M. J. Lighthill and G. B. Whitham, On kinematic waves: II. A theory of traffic flow on long crowded roads,, Proc. Roy. Soc., A229 (1955), 317.
doi: 10.1098/rspa.1955.0089. |
[38] |
T. Nagatani, The physics of traffic jams,, Rep. Prog. Phys., 65 (2002), 1331.
doi: 10.1088/0034-4885/65/9/203. |
[39] |
K. Nagel, Particle hopping models and traffic flow theory,, Phys. Rev. E, 53 (1996), 4655. Google Scholar |
[40] |
O. A. Oleinik, Discontinuous solutions of non-linear differential equations,, (Russian) Uspehi. Mat. Nauk., 12 (1957), 3.
|
[41] |
H. J. Payne, Models of freeway traffic and control,, "Simulation Councils Proc. Ser. : Mathematical Models of Public Systems,", 1 (1971), 51. Google Scholar |
[42] |
I. Prigogine and R. Herman, "Kinetic Theory of Vehicular Traffic,", American Elsevier Publishing Company Inc., (1971). Google Scholar |
[43] |
P. I. Richards, Shock waves on highway,, Operations Research, 4 (1956), 42.
doi: 10.1287/opre.4.1.42. |
[44] |
A. Sopasakis and M. Katsoulakis, Stochastic modeling and simulation of traffic flow: Asymmetric single exclusion process with Arrhenius look-ahead dynamics,, SIAM J. Appl. Math., 66 (2006), 921.
doi: 10.1137/040617790. |
[45] |
Lina Wang, Yaping Wu and Tong Li, Exponential stability of large-amplitude traveling fronts for quasi-linear relaxation systems with diffusion,, Physica D, 240 (2011), 971.
doi: 10.1016/j.physd.2011.02.003. |
[46] |
G. B. Whitham, "Linear and Nonlinear Waves,", Pure and Applied Mathematics. Wiley-Interscience [John Wiley & Sons], (1974).
|
[47] |
Lei Yu, Tong Li and Zhong-Ke Shi, Density waves in a traffic flow model with reactive-time delay,, Physica A, 389 (2010), 2607.
doi: 10.1016/j.physa.2010.03.009. |
[48] |
Lei Yu, Tong Li and Zhong-Ke Shi, The effect of diffusion in a new viscous continuum model,, Physics Letters, 374 (2010), 2346.
doi: 10.1016/j.physleta.2010.03.056. |
[49] |
H. M. Zhang, A non-equilibrium traffic model devoid of gas-like behavior,, Transportation Research, 36 (2002), 275.
doi: 10.1016/S0191-2615(00)00050-3. |
[50] |
H. M. Zhang, Driver memory, traffic viscosity and a viscous vehicular traffic flow model,, Transportation Research, 37 (2003), 27. Google Scholar |
[1] |
Wei Feng, Michael Freeze, Xin Lu. On competition models under allee effect: Asymptotic behavior and traveling waves. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5609-5626. doi: 10.3934/cpaa.2020256 |
[2] |
Zhenzhen Wang, Tianshou Zhou. Asymptotic behaviors and stochastic traveling waves in stochastic Fisher-KPP equations. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020323 |
[3] |
Wei-Chieh Chen, Bogdan Kazmierczak. Traveling waves in quadratic autocatalytic systems with complexing agent. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020364 |
[4] |
Ting Liu, Guo-Bao Zhang. Global stability of traveling waves for a spatially discrete diffusion system with time delay. Electronic Research Archive, , () : -. doi: 10.3934/era.2021003 |
[5] |
Jonathan J. Wylie, Robert M. Miura, Huaxiong Huang. Systems of coupled diffusion equations with degenerate nonlinear source terms: Linear stability and traveling waves. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 561-569. doi: 10.3934/dcds.2009.23.561 |
[6] |
Shuxing Chen, Jianzhong Min, Yongqian Zhang. Weak shock solution in supersonic flow past a wedge. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 115-132. doi: 10.3934/dcds.2009.23.115 |
[7] |
Caterina Balzotti, Simone Göttlich. A two-dimensional multi-class traffic flow model. Networks & Heterogeneous Media, 2020 doi: 10.3934/nhm.2020034 |
[8] |
Fioralba Cakoni, Pu-Zhao Kow, Jenn-Nan Wang. The interior transmission eigenvalue problem for elastic waves in media with obstacles. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020075 |
[9] |
Gui-Qiang Chen, Beixiang Fang. Stability of transonic shock-fronts in three-dimensional conical steady potential flow past a perturbed cone. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 85-114. doi: 10.3934/dcds.2009.23.85 |
[10] |
José Luiz Boldrini, Jonathan Bravo-Olivares, Eduardo Notte-Cuello, Marko A. Rojas-Medar. Asymptotic behavior of weak and strong solutions of the magnetohydrodynamic equations. Electronic Research Archive, 2021, 29 (1) : 1783-1801. doi: 10.3934/era.2020091 |
[11] |
Jong-Shenq Guo, Ken-Ichi Nakamura, Toshiko Ogiwara, Chang-Hong Wu. The sign of traveling wave speed in bistable dynamics. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3451-3466. doi: 10.3934/dcds.2020047 |
[12] |
Ran Zhang, Shengqiang Liu. On the asymptotic behaviour of traveling wave solution for a discrete diffusive epidemic model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1197-1204. doi: 10.3934/dcdsb.2020159 |
[13] |
Mohammad Ghani, Jingyu Li, Kaijun Zhang. Asymptotic stability of traveling fronts to a chemotaxis model with nonlinear diffusion. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021017 |
[14] |
Jerry L. Bona, Angel Durán, Dimitrios Mitsotakis. Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I. approximations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 87-111. doi: 10.3934/dcds.2020215 |
[15] |
Omid Nikan, Seyedeh Mahboubeh Molavi-Arabshai, Hossein Jafari. Numerical simulation of the nonlinear fractional regularized long-wave model arising in ion acoustic plasma waves. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020466 |
[16] |
Jason Murphy, Kenji Nakanishi. Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1507-1517. doi: 10.3934/dcds.2020328 |
[17] |
Yohei Yamazaki. Center stable manifolds around line solitary waves of the Zakharov–Kuznetsov equation with critical speed. Discrete & Continuous Dynamical Systems - A, 2021 doi: 10.3934/dcds.2021008 |
[18] |
Neng Zhu, Zhengrong Liu, Fang Wang, Kun Zhao. Asymptotic dynamics of a system of conservation laws from chemotaxis. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 813-847. doi: 10.3934/dcds.2020301 |
[19] |
Yueh-Cheng Kuo, Huey-Er Lin, Shih-Feng Shieh. Asymptotic dynamics of hermitian Riccati difference equations. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020365 |
[20] |
Joan Carles Tatjer, Arturo Vieiro. Dynamics of the QR-flow for upper Hessenberg real matrices. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1359-1403. doi: 10.3934/dcdsb.2020166 |
2019 Impact Factor: 1.053
Tools
Metrics
Other articles
by authors
[Back to Top]