Boundedness in a fully parabolic chemotaxis system with signal-dependent sensitivity and logistic term
- Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 61-68
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topMizukami, Masaaki. "Boundedness in a fully parabolic chemotaxis system with signal-dependent sensitivity and logistic term." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 61-68. <http://eudml.org/doc/294883>.
@inProceedings{Mizukami2017,
abstract = {},
author = {Mizukami, Masaaki},
booktitle = {Proceedings of Equadiff 14},
keywords = {Chemotaxis; signal-dependent sensitivity; logistic term; global existence.},
location = {Bratislava},
pages = {61-68},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {Boundedness in a fully parabolic chemotaxis system with signal-dependent sensitivity and logistic term},
url = {http://eudml.org/doc/294883},
year = {2017},
}
TY - CLSWK
AU - Mizukami, Masaaki
TI - Boundedness in a fully parabolic chemotaxis system with signal-dependent sensitivity and logistic term
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 61
EP - 68
AB -
KW - Chemotaxis; signal-dependent sensitivity; logistic term; global existence.
UR - http://eudml.org/doc/294883
ER -
References
top- Bellomo, N., Bellouquid, A., Tao, Y., Winkler, M., Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues, , Math. Models Methods Appl. Sci., 25, pp. 1663–1763, 2015. MR3351175
- Cao, X., Global bounded solutions of the higher-dimensional Keller–Segel system under smallness conditions in optimal spaces, , Discrete Contin. Dyn. Syst., 35, pp. 1891–1904, 2015. MR3294230
- Fujie, K., Boundedness in a fully parabolic chemotaxis system with singular sensitivity, , J.Math. Anal. Appl., 424, pp. 675–684, 2015. MR3286587
- Fujie, K., Study of reaction-diffusion systems modeling chemotaxis, , PhD thesis, Tokyo University of Science, 2016.
- Fujie, K., Senba, T., Global existence and boundedness of radial solutions to a two dimensional fully parabolic chemotaxis system with general sensitivity, , Nonlinearity, 29, pp. 2417–2450, 2016. MR3538418
- Fujie, K., Senba, T., A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system, , preprint. MR3816648
- He, X., Zheng, S., Convergence rate estimates of solutions in a higher dimensional chemotaxis system with logistic source, , J. Math. Anal. Appl., 436, pp. 970–982, 2016. MR3446989
- Horstmann, D., Wang, G., Blow-up in a chemotaxis model without symmetry assumptions, , Eur. J. Appl. Math., 12, pp. 159–177, 2001. MR1931303
- Lankeit, J., A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity, , Math. Methods Appl. Sci., 39, pp. 394–404, 2016. MR3454184
- Lankeit, J., Winkler, M., A generalized solution concept for the Keller–Segel system with logarithmic sensitivity: global solvability for large nonradial data, , NoDEA, Nonlinear Differ. Equ. Appl., 24, No. 4, Paper No. 49, 33 p., 2017. MR3674184
- Mizukami, M., Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity, , Discrete Contin. Dyn. Syst. Ser. B, 22, pp. 2301–2319, 2017. MR3664704
- Mizukami, M., Improvement of conditions for asymptotic stability in a two-species chemotaxis competition model with signal-dependent sensitivity, , submitted, arXiv:1706.04774[math.AP]. MR3664704
- Mizukami, M., Yokota, T., Global existence and asymptotic stability of solutions to a two-species chemotaxis system with any chemical diffusion, , J. Differential Equations, 261, pp. 2650–2669, 2016. MR3507983
- Mizukami, M., Yokota, T., A unified method for boundedness in fully parabolic chemotaxis systems with signal-dependent sensitivity, , Math. Nachr., to appear. MR3722501
- Nagai, T., Senba, T., Yoshida, K., Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis, , Funkcial. Ekvac., 40, pp. 411–433, 1997. MR1610709
- Negreanu, M., Tello, J. I., On a two species chemotaxis model with slow chemical diffusion, , SIAM J. Math. Anal., 46, pp. 3761–3781, 2014. MR3277217
- Negreanu, M., Tello, J. I., Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant, , J. Differential Equations, 258, pp. 1592–1617, 2015. MR3295594
- Winkler, M., Aggregation vs. global diffusive behavior in the higher-dimensional Keller–Segel model, , J. Differential Equations, 248, pp. 2889–2905, 2010. MR2644137
- Winkler, M., Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening, , J. Differential Equations, 257, pp. 1056–1077, 2014. MR3210023
- Zhang, Q., Li, X., Global existence and asymptotic properties of the solution to a two-species chemotaxis system, , J. Math. Anal. Appl., 418, pp. 47–63, 2014. MR3198865
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