Boundedness in a full parabolic two-species chemotaxis system

Comptes Rendus Mathematique - Tập 355 - Trang 80-83 - 2017
Myo Win Htwe1, Yifu Wang1
1School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, PR China

Tài liệu tham khảo

Alt, 1980, Orientation of cells migrating in a chemotactic gradient, vol. 38, 353 Bai, 2016, Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics, Indiana Univ. Math. J., 65, 553, 10.1512/iumj.2016.65.5776 Black, 2016, On the weakly competitive case in a two-species chemotaxis model, IMA J. Appl. Math., 81, 860, 10.1093/imamat/hxw036 Horstmann, 2003, From 1970 until present: the Keller–Segel model in chemotaxis and its consequences, I, Jahresber. Dtsch. Math.-Ver., 105, 103 Horstmann, 2011, Generalizing the Keller–Segel model: Lyapunov functionals, steady state analysis, and blow-up results for multi-species chemotaxis models in the presence of attraction and repulsion between competitive interacting species, J. Nonlinear Sci., 21, 231, 10.1007/s00332-010-9082-x Horstmann, 2005, Boundedness vs. blow-up in a chemotaxis system, J. Differ. Equ., 215, 52, 10.1016/j.jde.2004.10.022 Keller, 1970, Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol., 26, 399, 10.1016/0022-5193(70)90092-5 Li, 2015, Global bounded solutions and their asymptotic properties under small initial data condition in a two-dimensional chemotaxis system for two species, J. Math. Anal. Appl., 429, 1291, 10.1016/j.jmaa.2015.04.052 Lin, 2015, Boundedness in a two-species chemotaxis system, Math. Methods Appl. Sci., 38, 5085, 10.1002/mma.3429 Mizukami, 2016, Global existence and asymptotic stability of solutions to a two-species chemotaxis system with any chemical diffusion, J. Differ. Equ., 261, 2650, 10.1016/j.jde.2016.05.008 Negreanu, 2014, On a two species chemotaxis model with slow chemical diffusion, SIAM J. Math. Anal., 46, 3761, 10.1137/140971853 Negreanu, 2015, Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant, J. Differ. Equ., 258, 1592, 10.1016/j.jde.2014.11.009 Stinner, 2014, Competitive exclusion in a two species chemotaxis model, J. Math. Biol., 68, 1607, 10.1007/s00285-013-0681-7 Tello, 2012, Stabilization in a two-species chemotaxis system with logistic source, Nonlinearity, 25, 1413, 10.1088/0951-7715/25/5/1413 Winkler, 2010, Boundedness in the higher-dimensional parabolic–parabolic chemotaxis system with logistic source, Commun. Partial Differ. Equ., 35, 1516, 10.1080/03605300903473426 Winkler, 2010, Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity, Math. Nachr., 283, 1664, 10.1002/mana.200810838 Winkler, 2013, Finite-times blow-up in the higher-dimensional parabolic–parabolic Keller–Segel system, J. Math. Pures Appl., 100, 748, 10.1016/j.matpur.2013.01.020 Wolansky, 2002, Multi-components chemotactic system in absence of conflicts, Eur. J. Appl. Math., 13, 641, 10.1017/S0956792501004843 Zhang, 2015, Global boundedness of solutions to a two-species chemotaxis system, Z. Angew. Math. Phys., 66, 83, 10.1007/s00033-013-0383-4