Globally Bounded Solutions in A Chemotaxis Model of Quasilinear Parabolic Type

LIU Bing-chen, DONG Meng-zhen

doi:10.13371/j.cnki.chin.q.j.m.2019.03.005

Chinese Quarterly Journal of Mathematics >

2019 , Vol. 34 >Issue 3: 274 - 282

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2019.03.005

Globally Bounded Solutions in A Chemotaxis Model of Quasilinear Parabolic Type

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College of Science, China University of Petroleum

Received date: 2019-01-14

Online published: 2020-08-23

Supported by

supported by Shandong Provincial Natural Science Foundation,China(ZR2017LA003)

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Abstract

In this paper,we consider a quasilinear parabolic-parabolic chemotaxis model with nonlinear diffusivity,aggregation and logistic damping source: where k₁ e^pu≤D（u） or k₁ u^p≤D（u）;k₂ e^qu≤S（u）≤k₃ e^qu;g（u）≤a-be^ku.It is proved that,if q <k-1 or q=k-1 and b> b₀ for some constant b₀> 0,then there exists a unique classical solution which is globally bounded.The results show the effect of the aggregation and the logistic damping source on the existence of globally bounded solutions.

Key words： Chemotaxis; Nonlinear Diffusivity; Aggregation; Logistic Type Damping; Globally Bounded Solution

Cite this article

LIU Bing-chen, DONG Meng-zhen . Globally Bounded Solutions in A Chemotaxis Model of Quasilinear Parabolic Type[J]. Chinese Quarterly Journal of Mathematics, 2019 , 34(3) : 274 -282 . DOI: 10.13371/j.cnki.chin.q.j.m.2019.03.005

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