Global boundedness in a fully parabolic quasilinear chemotaxis system with singular sensitivity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:461

Article

Ding, Mengyao¹ 

[1] Peking Univ, Sch Math Sci, Beijing 100089, Peoples R China

关键词: Chemotaxis;    Nonlinear diffusion;    Global boundedness;    Signal-dependent sensitivity;   

DOI  :  10.1016/j.jmaa.2018.01.049

来源: Elsevier

【 摘 要 】

In this paper we study the global boundedness of solutions to the quasilinear fully parabolic chemotaxis system: ut = del.(D(u)del u-S(u)del phi(v)), v(t) = Delta v-v+u, where bounded domain Omega subset of R-n (n >= 2) subject to the non-flux boundary conditions, the diffusivity fulfills D(u) = a(0)(u+1)(-alpha) with a(0) > 0 and alpha >= 0, while the density-signal governed sensitivity satisfies 0 <= S(u) <= b(0)(u + 1)(beta) and 0 < phi'(v) <= chi/psi(k) for b(0), chi > 0 and beta, k is an element of R. It is shown that the solution is globally hounded provided alpha + beta < 1 and k <= 1. This result demonstrates the effect of sigtial-dependent sensitivity on the blow-up prevention. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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