-
Previous Article
Computational information for the logistic map at the chaos threshold
- DCDS-B Home
- This Issue
-
Next Article
Quasi periodic breathers in Hamiltonian lattices with symmetries
Well-posedness theory of an inhomogeneous traffic flow model
1. | Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419, United States |
The $L^1$ well-posedness theory for the model is established. In particular, we derive the continuous dependence of the solution on its initial data in $L^1$ topology. Moreover, the $L^1$-convergence to the unique zero relaxation limit is proved. Finally, the asymptotic states of a general solution whose initial data tend to constant states as $|x| \rightarrow +\infty$ are constructed.
[1] |
Guangrong Wu, Ping Zhang. The zero diffusion limit of 2-D Navier-Stokes equations with $L^1$ initial vorticity. Discrete and Continuous Dynamical Systems, 1999, 5 (3) : 631-638. doi: 10.3934/dcds.1999.5.631 |
[2] |
T. L. van Noorden, I. S. Pop, M. Röger. Crystal dissolution and precipitation in porous media: L$^1$-contraction and uniqueness. Conference Publications, 2007, 2007 (Special) : 1013-1020. doi: 10.3934/proc.2007.2007.1013 |
[3] |
Jiang Xu, Wen-An Yong. Zero-relaxation limit of non-isentropic hydrodynamic models for semiconductors. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1319-1332. doi: 10.3934/dcds.2009.25.1319 |
[4] |
Yong Xia, Yu-Jun Gong, Sheng-Nan Han. A new semidefinite relaxation for $L_{1}$-constrained quadratic optimization and extensions. Numerical Algebra, Control and Optimization, 2015, 5 (2) : 185-195. doi: 10.3934/naco.2015.5.185 |
[5] |
François Delarue, Franco Flandoli. The transition point in the zero noise limit for a 1D Peano example. Discrete and Continuous Dynamical Systems, 2014, 34 (10) : 4071-4083. doi: 10.3934/dcds.2014.34.4071 |
[6] |
Christian Rohde, Wenjun Wang, Feng Xie. Hyperbolic-hyperbolic relaxation limit for a 1D compressible radiation hydrodynamics model: superposition of rarefaction and contact waves. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2145-2171. doi: 10.3934/cpaa.2013.12.2145 |
[7] |
Nuno J. Alves, Athanasios E. Tzavaras. The relaxation limit of bipolar fluid models. Discrete and Continuous Dynamical Systems, 2022, 42 (1) : 211-237. doi: 10.3934/dcds.2021113 |
[8] |
Monica Motta, Caterina Sartori. On ${\mathcal L}^1$ limit solutions in impulsive control. Discrete and Continuous Dynamical Systems - S, 2018, 11 (6) : 1201-1218. doi: 10.3934/dcdss.2018068 |
[9] |
José Antonio Carrillo, Yingping Peng, Aneta Wróblewska-Kamińska. Relative entropy method for the relaxation limit of hydrodynamic models. Networks and Heterogeneous Media, 2020, 15 (3) : 369-387. doi: 10.3934/nhm.2020023 |
[10] |
Keonhee Lee, Kazumine Moriyasu, Kazuhiro Sakai. $C^1$-stable shadowing diffeomorphisms. Discrete and Continuous Dynamical Systems, 2008, 22 (3) : 683-697. doi: 10.3934/dcds.2008.22.683 |
[11] |
Yong-Kum Cho. On the Boltzmann equation with the symmetric stable Lévy process. Kinetic and Related Models, 2015, 8 (1) : 53-77. doi: 10.3934/krm.2015.8.53 |
[12] |
Seung-Yeal Ha, Mitsuru Yamazaki. $L^p$-stability estimates for the spatially inhomogeneous discrete velocity Boltzmann model. Discrete and Continuous Dynamical Systems - B, 2009, 11 (2) : 353-364. doi: 10.3934/dcdsb.2009.11.353 |
[13] |
Sze-Bi Hsu, Junping Shi. Relaxation oscillation profile of limit cycle in predator-prey system. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 893-911. doi: 10.3934/dcdsb.2009.11.893 |
[14] |
Yunhua Zhou. The local $C^1$-density of stable ergodicity. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2621-2629. doi: 10.3934/dcds.2013.33.2621 |
[15] |
José A. Carrillo, Laurent Desvillettes, Klemens Fellner. Fast-reaction limit for the inhomogeneous Aizenman-Bak model. Kinetic and Related Models, 2008, 1 (1) : 127-137. doi: 10.3934/krm.2008.1.127 |
[16] |
Jiang Xu, Ting Zhang. Zero-electron-mass limit of Euler-Poisson equations. Discrete and Continuous Dynamical Systems, 2013, 33 (10) : 4743-4768. doi: 10.3934/dcds.2013.33.4743 |
[17] |
Stefano Galatolo, Hugo Marsan. Quadratic response and speed of convergence of invariant measures in the zero-noise limit. Discrete and Continuous Dynamical Systems, 2021, 41 (11) : 5303-5327. doi: 10.3934/dcds.2021078 |
[18] |
Razvan C. Fetecau, Hui Huang, Daniel Messenger, Weiran Sun. Zero-diffusion limit for aggregation equations over bounded domains. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022078 |
[19] |
Xiangjun Wang, Jianghui Wen, Jianping Li, Jinqiao Duan. Impact of $\alpha$-stable Lévy noise on the Stommel model for the thermohaline circulation. Discrete and Continuous Dynamical Systems - B, 2012, 17 (5) : 1575-1584. doi: 10.3934/dcdsb.2012.17.1575 |
[20] |
Liyan Ma, Lionel Moisan, Jian Yu, Tieyong Zeng. A stable method solving the total variation dictionary model with $L^\infty$ constraints. Inverse Problems and Imaging, 2014, 8 (2) : 507-535. doi: 10.3934/ipi.2014.8.507 |
2021 Impact Factor: 1.497
Tools
Metrics
Other articles
by authors
[Back to Top]