Global boundedness to a parabolic-parabolic chemotaxis model with nonlinear diffusion and singular sensitivity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:475

Article

Jia, Zhe¹  Yang, Zuodong^1,2 

[1] Nanjing Normal Univ, Sch Math Sci, Inst Math, Nanjing 210023, Jiangsu, Peoples R China

[2] Nanjing Normal Univ, Sch Teacher Educ, Nanjing 210097, Jiangsu, Peoples R China

关键词: Chemotaxis;    Global boundedness;    Nonlinear diffusion;    Logistic source;    Singular sensitivity;   

DOI  :  10.1016/j.jmaa.2019.02.022

来源: Elsevier

【 摘 要 】

This article deals with the parabolic-parabolic chemotaxis system {u(t )= del . (D(u) del u) - del . (S(u)del phi (v)) + f(u), x is an element of Omega, t > 0, v(t) =Delta v - v + u, x is an element of Omega, t > 0 in a bounded domain Omega subset of R-n (n >= 1) with smooth boundary conditions, D, S is an element of C-2 ([0,+infinity)) nonnegative, with D(u) = a(0)(u + 1)(-alpha) for a(0) > 0 and alpha < 0, 0 <= S(u) <= b(0) (u +1)(beta) for b(0 )> 0, beta is an element of R, and where the singular sensitivity satisfies 0 < (phi' (v) <= chi/u(k) for chi > 0, k >= 1. In addition, f : R -> R is a smooth function satisfying f (s) (math) 0 or generalizing the logistic source f(s) = rs - mu s(m) for all s >= 0 with r is an element of R, mu > 0, and m > 1. It is shown that for the case without a growth source, if 2 beta - alpha < 2, the corresponding system possesses a globally bounded classical solution. For the case with a logistic source, if 2 beta + alpha < 2 and n = 1 or n >= 2 with m > 2 beta + 1, the corresponding system has a globally classical solution. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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