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Optimal control problems for quasivariational inequalities and its numerical approximation
Oscillating solutions to a parabolicelliptic system related to a chemotaxis model
1.  Department of Mathematics, Faculty of Sciences, Ehime University, Matsuyama, 7908577, Japan 
2.  Faculty of Engineering, Kyushu Institute of Technology, Kitakyushu, 8048550, Japan 
[1] 
Alina Chertock, Alexander Kurganov, Mária LukáčováMedvi${\rm{\check{d}}}$ová, Șeyma Nur Özcan. An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions. Kinetic & Related Models, 2019, 12 (1) : 195216. doi: 10.3934/krm.2019009 
[2] 
Piotr Biler, Tomasz Cieślak, Grzegorz Karch, Jacek Zienkiewicz. Local criteria for blowup in twodimensional chemotaxis models. Discrete & Continuous Dynamical Systems  A, 2017, 37 (4) : 18411856. doi: 10.3934/dcds.2017077 
[3] 
T. Tachim Medjo. The exponential behavior of the stochastic primitive equations in two dimensional space with multiplicative noise. Discrete & Continuous Dynamical Systems  B, 2010, 14 (1) : 177197. doi: 10.3934/dcdsb.2010.14.177 
[4] 
Qingshan Zhang, Yuxiang Li. Convergence rates of solutions for a twodimensional chemotaxisNavierStokes system. Discrete & Continuous Dynamical Systems  B, 2015, 20 (8) : 27512759. doi: 10.3934/dcdsb.2015.20.2751 
[5] 
Yulan Wang. Global solvability in a twodimensional selfconsistent chemotaxisNavierStokes system. Discrete & Continuous Dynamical Systems  S, 2018, 0 (0) : 329349. doi: 10.3934/dcdss.2020019 
[6] 
Laiqing Meng, Jia Yuan, Xiaoxin Zheng. Global existence of almost energy solution to the twodimensional chemotaxisNavierStokes equations with partial diffusion. Discrete & Continuous Dynamical Systems  A, 2019, 39 (6) : 34133441. doi: 10.3934/dcds.2019141 
[7] 
Toshiyuki Suzuki. Nonlinear Schrödinger equations with inversesquare potentials in two dimensional space. Conference Publications, 2015, 2015 (special) : 10191024. doi: 10.3934/proc.2015.1019 
[8] 
Yūki Naito, Takasi Senba. Bounded and unbounded oscillating solutions to a parabolicelliptic system in two dimensional space. Communications on Pure & Applied Analysis, 2013, 12 (5) : 18611880. doi: 10.3934/cpaa.2013.12.1861 
[9] 
ShinIchiro Ei, Hirofumi Izuhara, Masayasu Mimura. Infinite dimensional relaxation oscillation in aggregationgrowth systems. Discrete & Continuous Dynamical Systems  B, 2012, 17 (6) : 18591887. doi: 10.3934/dcdsb.2012.17.1859 
[10] 
DongHo Tsai, ChiaHsing Nien. On the oscillation behavior of solutions to the onedimensional heat equation. Discrete & Continuous Dynamical Systems  A, 2019, 39 (7) : 40734089. doi: 10.3934/dcds.2019164 
[11] 
Shen Bian, Li Chen, Evangelos A. Latos. Chemotaxis model with nonlocal nonlinear reaction in the whole space. Discrete & Continuous Dynamical Systems  A, 2018, 38 (10) : 50675083. doi: 10.3934/dcds.2018222 
[12] 
Alexander Kurganov, Mária LukáčováMedvidová. Numerical study of twospecies chemotaxis models. Discrete & Continuous Dynamical Systems  B, 2014, 19 (1) : 131152. doi: 10.3934/dcdsb.2014.19.131 
[13] 
Xie Li, Yilong Wang. Boundedness in a twospecies chemotaxis parabolic system with two chemicals. Discrete & Continuous Dynamical Systems  B, 2017, 22 (7) : 27172729. doi: 10.3934/dcdsb.2017132 
[14] 
Liangchen Wang, Jing Zhang, Chunlai Mu, Xuegang Hu. Boundedness and stabilization in a twospecies chemotaxis system with two chemicals. Discrete & Continuous Dynamical Systems  B, 2017, 22 (11) : 131. doi: 10.3934/dcdsb.2019178 
[15] 
Tao Wang, Huijiang Zhao, Qingyang Zou. Onedimensional compressible NavierStokes equations with large density oscillation. Kinetic & Related Models, 2013, 6 (3) : 649670. doi: 10.3934/krm.2013.6.649 
[16] 
ZhiAn Wang, Kun Zhao. Global dynamics and diffusion limit of a onedimensional repulsive chemotaxis model. Communications on Pure & Applied Analysis, 2013, 12 (6) : 30273046. doi: 10.3934/cpaa.2013.12.3027 
[17] 
Youshan Tao. Global dynamics in a higherdimensional repulsion chemotaxis model with nonlinear sensitivity. Discrete & Continuous Dynamical Systems  B, 2013, 18 (10) : 27052722. doi: 10.3934/dcdsb.2013.18.2705 
[18] 
Johannes Lankeit, Yulan Wang. Global existence, boundedness and stabilization in a highdimensional chemotaxis system with consumption. Discrete & Continuous Dynamical Systems  A, 2017, 37 (12) : 60996121. doi: 10.3934/dcds.2017262 
[19] 
Tong Li, Anthony Suen. Existence of intermediate weak solution to the equations of multidimensional chemotaxis systems. Discrete & Continuous Dynamical Systems  A, 2016, 36 (2) : 861875. doi: 10.3934/dcds.2016.36.861 
[20] 
Hua Zhong, Chunlai Mu, Ke Lin. Global weak solution and boundedness in a threedimensional competing chemotaxis. Discrete & Continuous Dynamical Systems  A, 2018, 38 (8) : 38753898. doi: 10.3934/dcds.2018168 
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