Boundedness enforced by mildly saturated conversion in a chemotaxis-May Nowak model for virus infection

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:472

Article

Fuest, Mario¹ 

[1] Univ Paderborn, Inst Math, D-33098 Paderborn, Germany

关键词: Boundedness;    Chemotaxis;    May-Nowak model;    Virus dynamics;   

DOI  :  10.1016/j.jmaa.2018.12.020

来源: Elsevier

【 摘 要 】

We study the system {u(t) = Delta(u) - del . (u del v) - u - f(u)w + kappa, v(t) = Delta v - v + f(u)w, w(t) = Delta w - w + v, (star) which models the virus dynamics in an early stage of an HIV infection, in a smooth, bounded domain Omega subset of R-n, n is an element of N, for a parameter kappa >= 0 and a given function f is an element of C-1 ([0, infinity)) satisfying f >= 0, f (0) = 0 and f(s) <= K(f)s(alpha) for all s >= 1, some K-f > 0 and alpha is an element of R. We prove that whenever alpha < 2/n, solutions to (star) exist globally and are bounded. The proof mainly relies on smoothing estimates for the Neumann heat semigroup and (in the case alpha > 1) on a functional inequality. Furthermore, we provide some indication why the exponent 2/n could be essentially optimal. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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