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Stability of constant states and qualitative behavior of solutions to a one dimensional hyperbolic model of chemotaxis
Particle, kinetic and fluid models for phototaxis
1.  Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151747 
2.  Department of Mathematics and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, MD 20742 
[1] 
Lining Ru, Xiaoping Xue. Flocking of CuckerSmale model with intrinsic dynamics. Discrete & Continuous Dynamical Systems  B, 2019, 24 (12) : 68176835. doi: 10.3934/dcdsb.2019168 
[2] 
ChiunChuan Chen, SeungYeal Ha, Xiongtao Zhang. The global wellposedness of the kinetic CuckerSmale flocking model with chemotactic movements. Communications on Pure & Applied Analysis, 2018, 17 (2) : 505538. doi: 10.3934/cpaa.2018028 
[3] 
Martial Agueh, Reinhard Illner, Ashlin Richardson. Analysis and simulations of a refined flocking and swarming model of CuckerSmale type. Kinetic & Related Models, 2011, 4 (1) : 116. doi: 10.3934/krm.2011.4.1 
[4] 
SeungYeal Ha, Jinwook Jung, Peter Kuchling. Emergence of anomalous flocking in the fractional CuckerSmale model. Discrete & Continuous Dynamical Systems  A, 2019, 39 (9) : 54655489. doi: 10.3934/dcds.2019223 
[5] 
ChunHsien Li, SuhYuh Yang. A new discrete CuckerSmale flocking model under hierarchical leadership. Discrete & Continuous Dynamical Systems  B, 2016, 21 (8) : 25872599. doi: 10.3934/dcdsb.2016062 
[6] 
YuJhe Huang, ZhongFu Huang, Jonq Juang, YuHao Liang. Flocking of nonidentical CuckerSmale models on general coupling network. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020155 
[7] 
Zhisu Liu, Yicheng Liu, Xiang Li. Flocking and lineshaped spatial configuration to delayed CuckerSmale models. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020253 
[8] 
Jan Haskovec, Ioannis Markou. Asymptotic flocking in the CuckerSmale model with reactiontype delays in the nonoscillatory regime. Kinetic & Related Models, 2020, 13 (4) : 795813. doi: 10.3934/krm.2020027 
[9] 
Martin Friesen, Oleksandr Kutoviy. Stochastic CuckerSmale flocking dynamics of jumptype. Kinetic & Related Models, 2020, 13 (2) : 211247. doi: 10.3934/krm.2020008 
[10] 
HyeongOhk Bae, YoungPil Choi, SeungYeal Ha, MoonJin Kang. Asymptotic flocking dynamics of CuckerSmale particles immersed in compressible fluids. Discrete & Continuous Dynamical Systems  A, 2014, 34 (11) : 44194458. doi: 10.3934/dcds.2014.34.4419 
[11] 
MoonJin Kang, SeungYeal Ha, Jeongho Kim, Woojoo Shim. Hydrodynamic limit of the kinetic thermomechanical CuckerSmale model in a strong local alignment regime. Communications on Pure & Applied Analysis, 2020, 19 (3) : 12331256. doi: 10.3934/cpaa.2020057 
[12] 
SeungYeal Ha, Bora Moon. Quantitative local sensitivity estimates for the random kinetic CuckerSmale model with chemotactic movement. Kinetic & Related Models, 2020, 13 (5) : 889931. doi: 10.3934/krm.2020031 
[13] 
Huyên Pham. Linear quadratic optimal control of conditional McKeanVlasov equation with random coefficients and applications. Probability, Uncertainty and Quantitative Risk, 2016, 1 (0) : 7. doi: 10.1186/s415460160008x 
[14] 
Jean Dolbeault. An introduction to kinetic equations: the VlasovPoisson system and the Boltzmann equation. Discrete & Continuous Dynamical Systems  A, 2002, 8 (2) : 361380. doi: 10.3934/dcds.2002.8.361 
[15] 
YoungPil Choi, Samir Salem. CuckerSmale flocking particles with multiplicative noises: Stochastic meanfield limit and phase transition. Kinetic & Related Models, 2019, 12 (3) : 573592. doi: 10.3934/krm.2019023 
[16] 
SeungYeal Ha, Doheon Kim, Weiyuan Zou. Slow flocking dynamics of the CuckerSmale ensemble with a chemotactic movement in a temperature field. Kinetic & Related Models, 2020, 13 (4) : 759793. doi: 10.3934/krm.2020026 
[17] 
SeungYeal Ha, Shi Jin. Local sensitivity analysis for the CuckerSmale model with random inputs. Kinetic & Related Models, 2018, 11 (4) : 859889. doi: 10.3934/krm.2018034 
[18] 
Marco Caponigro, Massimo Fornasier, Benedetto Piccoli, Emmanuel Trélat. Sparse stabilization and optimal control of the CuckerSmale model. Mathematical Control & Related Fields, 2013, 3 (4) : 447466. doi: 10.3934/mcrf.2013.3.447 
[19] 
YoungPil Choi, Jan Haskovec. CuckerSmale model with normalized communication weights and time delay. Kinetic & Related Models, 2017, 10 (4) : 10111033. doi: 10.3934/krm.2017040 
[20] 
SeungYeal Ha, Dongnam Ko, Yinglong Zhang. Remarks on the critical coupling strength for the CuckerSmale model with unit speed. Discrete & Continuous Dynamical Systems  A, 2018, 38 (6) : 27632793. doi: 10.3934/dcds.2018116 
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