A note for global existence of a two-dimensional chemotaxis haptotaxis model with remodeling of non-diffusible attractant

作者：Ke, Yuanyuan; Zheng, Jiashan^*

来源：Nonlinearity, 2018, 31(10): 4602-4620.

DOI：10.1088/1361-6544/aad307

• chemotaxis haptotaxis
• global existence
• non-diffusible attractant

In this paper, we study the following coupled chemotaxis-hapioffixis model with remodeling of non-diffusible attractant
{u(t) = Delta u - chi del .(u del v) - xi del .(u del w) + mu u (1 - u -w), v(t) = Delta v - v + u, w(t) = -uw + eta w(1 - u - w)
in a bounded smooth domain Omega subset of R-2 zero-flux boundary conditions, where chi, xi and eta) are positive parameters. Under appropriate regularity assumptions on the initial data (u(0), v(0), w(0)), by developing some L-p-estimate techniques, we prove the global existence and uniqueness of classical solutions when mu > 0, where mu is the logistic growth rate of cancer cells. This result removes the additional restriction on mu, where mu is sufficiently large in Pang and Wang (2017 J. Differ. Equ. 263 1269-92) for the global existence of solutions.

• 出版日期2018-10
• 单位鲁东大学; 中国人民大学