References
- N. Bellomo, A. Bellouquid, Y. Tao and M. Winkler. Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues. Mathematical Models and Methods in Applied Sciences, 25(9):1663–1763, 2015. https://doi.org/10.1142/S021820251550044X.
- X.Y. Chen and W.A. Liu. Global attractor for a density-dependent sensitivity chemotaxis model. Acta Mathematica Scientia, 32B(4):1365–1375, 2012.
- X.Y. Chen and Y. Yang. Existence of the traveling wave solutions for a chemotaxis equations. Acta Mathematica Sinica, Chinese Series, 55(5):817–828, 2012. doi: 10.6023/A1112251
- R. Čiegis and A. Bugajev. Numerical approximation of one model of the bacterial self-organization. Nonlinear Analysis: Modelling and Control, 17(3):253–270, 2012.
- D. Horstmann and M. Winkler. Boundedness vs. blow-up in a chemotaxis system. Journal of Differential Equations, 215(1):52–107, 2005. https://doi.org/10.1016/j.jde.2004.10.022.
- E.F. Keller and L.A. Segel. Initiation of slime mold aggregation viewed as an instability. Journal of Theoretical Biology, 26(3):399–415, 1970. https://doi.org/10.1016/0022-5193(70)90092-5. doi: 10.1016/0022-5193(70)90092-5
- X. Mora. Semilinear parabolic problems define semiflows on ck spaces. Transactions of the American Mathematical Society, 278(1):21–55, 1983.
- A. Pazy. Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, New York, 1983. https://doi.org/10.1007/978-1-4612-5561-1.
- Y.S. Tao and M. Winkler. Eventual smoothness and stabilization of largedata solutions in a three-dimensional chemotaxis system with consumption of chemoattractant. Journal of Differential Equations, 252(3):2520–2543, 2012. https://doi.org/10.1016/j.jde.2011.07.010.
- M. Winkler. Global large-data solutions in a chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops. Communications in Partial Differential Equations, 37(2):319–351, 2012. https://doi.org/10.1080/03605302.2011.591865.
- M. Winkler. Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system. Journal de Mathématiques Pures et Appliqués, 100(5):748–767, 2013. https://doi.org/10.1016/j.matpur.2013.01.020.