Dampening effect of logistic source in a two-dimensional haptotaxis system with nonlinear zero-order interaction

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:492

Article

Chen, Zhen¹ 

[1] Donghua Univ, Sch Informat Sci & Technol, Shanghai 200051, Peoples R China

关键词: Haptotaxis;    Logistic source;    Boundedness;    Stabilization;   

DOI  :  10.1016/j.jmaa.2020.124435

来源: Elsevier

【 摘 要 】

This paper deals with the oncolytic virotherapy model {u(t) = Delta u - del . (u del v) - uz + mu u(1 - u), v(t) = -(u + w)v, (*) w(t) = D-w Delta w - w + uz, z(t) = D-z Delta z - z - uz + beta w, in a bounded domain Omega subset of R-2 with smooth boundary, where mu, D-w, D-z and beta are prescribed positive parameters. For any given suitably regular initial data, the global existence of classical solution to the corresponding homogeneous Neumann initial-boundary problem for a more general model allowing mu = 0 was previously verified in Tao and Winkler (2020) [15]. This work further shows that whenever mu > 0, the above-mentioned global classical solution to (*) is uniformly bounded; and moreover, if beta < 1, then the solution (u, v, w, z) stabilizes to the constant equilibrium (1,0,0,0) in the topology L-p (Omega) x (L-infinity(Omega))(3) with any p > 1 in a large time limit. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free