https://orcid.org/0000-0001-9963-0800
References
- Horstmann D, Wang G. Blow-up in a chemotaxis model without symmetry assumptions. Eur J Appl Math. 2001;12:159–177. doi: 10.1017/S0956792501004363
- Nagai T, Senba T, Suzuki T. Chemotactic collapse in a parabolic system of mathematical biology. Hiroshima Math J. 2000;30:463–497. doi: 10.32917/hmj/1206124609
- Feireisl E, Laurençt P, Petzeltová H. On convergence to equilibria for the Keller–Segel chemotaxis model. J Differ Equ. 2010;236:551–569. doi: 10.1016/j.jde.2007.02.002
- Biler P. Local and global solvability of some parabolic systems modelling chemotaxis. Adv Math Sci Appl. 1998;8(2):715–743.
- Schaaf R. Stationary solutions of chemotaxis systems. Trans Am Math Soc. 1985;292(2):531–556. doi: 10.1090/S0002-9947-1985-0808736-1
- Senba T, Suzuki T. Some structures of the solution set for a stationary system of chemotaxis. Adv Math Sci Appl. 2000;10(1):191–224.
- Hillen T, Painter T. A user's guide to PDE models for chemotaxis. J Math Biol. 2009;58(183–217. doi: 10.1007/s00285-008-0201-3
- Biler P. Global solutions to some parabolic-elliptic systems of chemotaxis. Adv Math Sci Appl. 1999;9(1):347–359.
- Fujie K. Boundedness in a fully parabolic chemotaxis system with singular sensitivity. J Math Anal Appl. 2015;424:675–684. doi: 10.1016/j.jmaa.2014.11.045
- Lankeit J. A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity. Math Methods Appl Sci. 2016;39:394–404. doi: 10.1002/mma.3489
- Winkler M. Global solutions in a fully parabolic chemotaxis system with singular sensitivity. Math Methods Appl Sci. 2011;34:176–190. doi: 10.1002/mma.1346
- Fujie K, Senba T. Global existence and boundedness of radial solutions to a two dimensional fully parabolic chemotaxis system with general sensitivity. Nonlinearity. 2016;29:2417–2450. doi: 10.1088/0951-7715/29/8/2417
- Fujie K, Senba T. A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic–parabolic chemotaxis system. Nonlinearity. 2018;31:1639–1672. doi: 10.1088/1361-6544/aaa2df
- Lankeit J, Winkler M. A generalized solution concept for the Keller–Segel system with logarithmic sensitivity: global solvability for large nonradial data. Nonlinear Differ Equ Appl. 2017;24: 24:49. doi: 10.1007/s00030-017-0472-8
- Stinner C, Winkler M. Global weak solutions in a chemotaxis system with large singular sensitivity. Nonlinear Anal Real World Appl. 2011;12:3727–3740.
- Zhigun A, Generalised supersolutions with mass control for the Keller–Segel system with logarithmic sensitivity. J Math Anal Appl. 2018;467(2):1270–1286. doi: 10.1016/j.jmaa.2018.08.001
- Winkler M, Yokota T. Stabilization in the logarithmic Keller–Segel system. Nonlinear Anal. 2018;170:123–141. doi: 10.1016/j.na.2018.01.002
- Winkler M. Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller–Segel system. J Math Pures Appl. 2013;100:748–767. doi: 10.1016/j.matpur.2013.01.020
- Mizukami M, Yokota T. A unified method for boundedness in fully parabolic chemotaxis systems with signal-dependent sensitivity. Math Nachr. 2017;290:2648–2660. doi: 10.1002/mana.201600399
- Henry D. Geometric Theory of Semilinear Parabolic Equations. Berlin-New York: Springer-Verlag; 1981; Lecture Notes in Mathematics, Vol. 840.
- Winkler M. Aggregation vs. global diffusive behavior in the higher-dimensional Keller–Segel model. J Differ Equ. 2010;248:2889–2905. doi: 10.1016/j.jde.2010.02.008