Large-Data Solutions in a Three-Dimensional Chemotaxis-Haptotaxis System with Remodeling of Non-diffusible Attractant: The Role of Sub-linear Production of Diffusible Signal

作者：Chen, Zhen; Tao, Youshan^*

来源：Acta Applicandae Mathematicae, 2019, 163(1): 129-143.

DOI：10.1007/s10440-018-0216-8

• Chemotaxis
• Haptotaxis
• Sub-linear production of signal
• Logistic proliferation
• Tissue remodeling

This work considers the chemotaxis-haptotaxis system @@@ {u(t) = Delta u - chi del center dot (u del v) - xi del (u del w)+ mu u(1 - u - w), @@@ v(t) = Delta v - v + f (u) g(w), @@@ w(t) = -vw + eta w(1 - u - w), @@@ in a bounded convex domain Omega subset of R-3 with smooth boundary, where chi, xi, mu and eta are positive parameters, f and g are prescribed nonnegative and C-1-smooth functions and f fulfills @@@ f(s) <= Ks(alpha) for all s >= 0 with some positive constant K and parameter alpha is an element of (0, 1]. It is shown that whenever @@@ 0 < alpha < 5/6, @@@ for any given suitably regular initial data the corresponding Neumann initial-boundary problem possesses a unique global-in-time classical solution that is uniformly bounded.

• 出版日期2019-10
• 单位东华大学