Volume 17, Issue 4
Dynamical Behaviors of Attraction-Repulsion Chemotaxis Model

Xinmei Wen, Mingyue ZhangYang Chen

Int. J. Numer. Anal. Mod., 17 (2020), pp. 457-484.

Published online: 2020-08

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  • Abstract

A free boundary problem for the chemotaxis model of parabolic-elliptic type is investigated in the present paper, which can be used to simulate the dynamics of cell density under the influence of the nonlinear diffusion and nonlocal attraction-repulsion forces. In particular, it is shown for supercritical case that if the initial total mass of cell density is small enough or the interaction between repulsion and attraction cancels almost each other, the strong solution for the cell density exists globally in time and converges to the self-similar Barenblatt solution at the algebraic time rate, and for subcritical case that if the initial data is a small perturbation of the steady-state solution and the attraction effect dominates the process, the strong solution for cell density exists globally in time and converges to the steady-state solution at the exponential time rate.

  • Keywords

Chemotaxis, free boundary problem, Barenblatt solution, steady-state solution.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-17-457, author = {Wen , Xinmei and Zhang , Mingyue and Chen , Yang}, title = {Dynamical Behaviors of Attraction-Repulsion Chemotaxis Model}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {4}, pages = {457--484}, abstract = {

A free boundary problem for the chemotaxis model of parabolic-elliptic type is investigated in the present paper, which can be used to simulate the dynamics of cell density under the influence of the nonlinear diffusion and nonlocal attraction-repulsion forces. In particular, it is shown for supercritical case that if the initial total mass of cell density is small enough or the interaction between repulsion and attraction cancels almost each other, the strong solution for the cell density exists globally in time and converges to the self-similar Barenblatt solution at the algebraic time rate, and for subcritical case that if the initial data is a small perturbation of the steady-state solution and the attraction effect dominates the process, the strong solution for cell density exists globally in time and converges to the steady-state solution at the exponential time rate.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/17865.html} }
TY - JOUR T1 - Dynamical Behaviors of Attraction-Repulsion Chemotaxis Model AU - Wen , Xinmei AU - Zhang , Mingyue AU - Chen , Yang JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 457 EP - 484 PY - 2020 DA - 2020/08 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/17865.html KW - Chemotaxis, free boundary problem, Barenblatt solution, steady-state solution. AB -

A free boundary problem for the chemotaxis model of parabolic-elliptic type is investigated in the present paper, which can be used to simulate the dynamics of cell density under the influence of the nonlinear diffusion and nonlocal attraction-repulsion forces. In particular, it is shown for supercritical case that if the initial total mass of cell density is small enough or the interaction between repulsion and attraction cancels almost each other, the strong solution for the cell density exists globally in time and converges to the self-similar Barenblatt solution at the algebraic time rate, and for subcritical case that if the initial data is a small perturbation of the steady-state solution and the attraction effect dominates the process, the strong solution for cell density exists globally in time and converges to the steady-state solution at the exponential time rate.

Xinmei Wen, Mingyue Zhang & Yang Chen. (2020). Dynamical Behaviors of Attraction-Repulsion Chemotaxis Model. International Journal of Numerical Analysis and Modeling. 17 (4). 457-484. doi:
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