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Well-posedness for a class of nonlinear degenerate parabolic equations
Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with the sensitivity $v^{-1}S(u)$
1. | Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan, Japan |
References:
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References:
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Xie Li, Zhaoyin Xiang. Boundedness in quasilinear Keller-Segel equations with nonlinear sensitivity and logistic source. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3503-3531. doi: 10.3934/dcds.2015.35.3503 |
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Hao Yu, Wei Wang, Sining Zheng. Boundedness of solutions to a fully parabolic Keller-Segel system with nonlinear sensitivity. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1635-1644. doi: 10.3934/dcdsb.2017078 |
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Hao Yu, Wei Wang, Sining Zheng. Global boundedness of solutions to a Keller-Segel system with nonlinear sensitivity. Discrete and Continuous Dynamical Systems - B, 2016, 21 (4) : 1317-1327. doi: 10.3934/dcdsb.2016.21.1317 |
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Mengyao Ding, Xiangdong Zhao. $ L^\sigma $-measure criteria for boundedness in a quasilinear parabolic-parabolic Keller-Segel system with supercritical sensitivity. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5297-5315. doi: 10.3934/dcdsb.2019059 |
[5] |
Mengyao Ding, Sining Zheng. $ L^γ$-measure criteria for boundedness in a quasilinear parabolic-elliptic Keller-Segel system with supercritical sensitivity. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 2971-2988. doi: 10.3934/dcdsb.2018295 |
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Kentarou Fujie, Takasi Senba. Global existence and boundedness in a parabolic-elliptic Keller-Segel system with general sensitivity. Discrete and Continuous Dynamical Systems - B, 2016, 21 (1) : 81-102. doi: 10.3934/dcdsb.2016.21.81 |
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Qi Wang, Jingyue Yang, Feng Yu. Boundedness in logistic Keller-Segel models with nonlinear diffusion and sensitivity functions. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 5021-5036. doi: 10.3934/dcds.2017216 |
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Sachiko Ishida, Tomomi Yokota. Boundedness in a quasilinear fully parabolic Keller-Segel system via maximal Sobolev regularity. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 211-232. doi: 10.3934/dcdss.2020012 |
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Sachiko Ishida. An iterative approach to $L^\infty$-boundedness in quasilinear Keller-Segel systems. Conference Publications, 2015, 2015 (special) : 635-643. doi: 10.3934/proc.2015.0635 |
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Tobias Black. Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 119-137. doi: 10.3934/dcdss.2020007 |
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Wenji Zhang. Global generalized solvability in the Keller-Segel system with singular sensitivity and arbitrary superlinear degradation. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022121 |
[12] |
Qi Wang. Boundary spikes of a Keller-Segel chemotaxis system with saturated logarithmic sensitivity. Discrete and Continuous Dynamical Systems - B, 2015, 20 (4) : 1231-1250. doi: 10.3934/dcdsb.2015.20.1231 |
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Jaewook Ahn, Kyungkeun Kang. On a Keller-Segel system with logarithmic sensitivity and non-diffusive chemical. Discrete and Continuous Dynamical Systems, 2014, 34 (12) : 5165-5179. doi: 10.3934/dcds.2014.34.5165 |
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Miaoqing Tian, Sining Zheng. Global boundedness versus finite-time blow-up of solutions to a quasilinear fully parabolic Keller-Segel system of two species. Communications on Pure and Applied Analysis, 2016, 15 (1) : 243-260. doi: 10.3934/cpaa.2016.15.243 |
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Hongyun Peng, Zhi-An Wang, Kun Zhao, Changjiang Zhu. Boundary layers and stabilization of the singular Keller-Segel system. Kinetic and Related Models, 2018, 11 (5) : 1085-1123. doi: 10.3934/krm.2018042 |
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Dan Li, Chunlai Mu, Pan Zheng, Ke Lin. Boundedness in a three-dimensional Keller-Segel-Stokes system involving tensor-valued sensitivity with saturation. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 831-849. doi: 10.3934/dcdsb.2018209 |
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Johannes Lankeit. Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 233-255. doi: 10.3934/dcdss.2020013 |
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Jan Burczak, Rafael Granero-Belinchón. Boundedness and homogeneous asymptotics for a fractional logistic Keller-Segel equations. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 139-164. doi: 10.3934/dcdss.2020008 |
[19] |
Hai-Yang Jin. Boundedness and large time behavior in a two-dimensional Keller-Segel-Navier-Stokes system with signal-dependent diffusion and sensitivity. Discrete and Continuous Dynamical Systems, 2018, 38 (7) : 3595-3616. doi: 10.3934/dcds.2018155 |
[20] |
Ping Liu, Junping Shi, Zhi-An Wang. Pattern formation of the attraction-repulsion Keller-Segel system. Discrete and Continuous Dynamical Systems - B, 2013, 18 (10) : 2597-2625. doi: 10.3934/dcdsb.2013.18.2597 |
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