Boundedness in a quasilinear fully parabolic Keller–Segel system with logistic source

Yifu Wang; Ji Liu

doi:10.1016/j.nonrwa.2017.04.010

Boundedness in a quasilinear fully parabolic Keller–Segel system with logistic source

Yifu Wang
, Ji Liu^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

In this paper, we consider the quasilinear chemotaxis system (⋆){u_t=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),x∈Ω,t>0,v_t=Δv−v+u,x∈Ω,t>0 in a bounded domain Ω⊂Rⁿ(n≥2) under zero-flux boundary conditions, where the nonlinearities D,S∈C²([0,∞)) are supposed to generalize the prototypes D(u)=C_D(u+1)^m−1andS(u)=C_Su(u+1)^q−1 with C_D,C_S>0 and m,q∈R, and f∈C¹([0,∞)) satisfies f(u)≤r−bu^γ with r≥0,b>0 and γ>1. It is shown that if [Formula presented], then (⋆) has a unique globally bounded classical solution.

Original language	English
Pages (from-to)	113-130
Number of pages	18
Journal	Nonlinear Analysis: Real World Applications
Volume	38
DOIs	https://doi.org/10.1016/j.nonrwa.2017.04.010
Publication status	Published - 1 Dec 2017

Keywords

Boundedness
Chemotaxis
Logistic source
Quasilinear

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10.1016/j.nonrwa.2017.04.010

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@article{1860594332dd42d3818969ddb88d7a7b,

title = "Boundedness in a quasilinear fully parabolic Keller–Segel system with logistic source",

abstract = "In this paper, we consider the quasilinear chemotaxis system (⋆)\{ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),x∈Ω,t>0,vt=Δv−v+u,x∈Ω,t>0 in a bounded domain Ω⊂Rn(n≥2) under zero-flux boundary conditions, where the nonlinearities D,S∈C2([0,∞)) are supposed to generalize the prototypes D(u)=CD(u+1)m−1andS(u)=CSu(u+1)q−1 with CD,CS>0 and m,q∈R, and f∈C1([0,∞)) satisfies f(u)≤r−buγ with r≥0,b>0 and γ>1. It is shown that if [Formula presented], then (⋆) has a unique globally bounded classical solution.",

keywords = "Boundedness, Chemotaxis, Logistic source, Quasilinear",

author = "Yifu Wang and Ji Liu",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Ltd",

year = "2017",

month = dec,

day = "1",

doi = "10.1016/j.nonrwa.2017.04.010",

language = "English",

volume = "38",

pages = "113--130",

journal = "Nonlinear Analysis: Real World Applications",

issn = "1468-1218",

publisher = "Elsevier B.V.",

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TY - JOUR

T1 - Boundedness in a quasilinear fully parabolic Keller–Segel system with logistic source

AU - Wang, Yifu

AU - Liu, Ji

PY - 2017/12/1

Y1 - 2017/12/1

N2 - In this paper, we consider the quasilinear chemotaxis system (⋆){ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),x∈Ω,t>0,vt=Δv−v+u,x∈Ω,t>0 in a bounded domain Ω⊂Rn(n≥2) under zero-flux boundary conditions, where the nonlinearities D,S∈C2([0,∞)) are supposed to generalize the prototypes D(u)=CD(u+1)m−1andS(u)=CSu(u+1)q−1 with CD,CS>0 and m,q∈R, and f∈C1([0,∞)) satisfies f(u)≤r−buγ with r≥0,b>0 and γ>1. It is shown that if [Formula presented], then (⋆) has a unique globally bounded classical solution.

AB - In this paper, we consider the quasilinear chemotaxis system (⋆){ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),x∈Ω,t>0,vt=Δv−v+u,x∈Ω,t>0 in a bounded domain Ω⊂Rn(n≥2) under zero-flux boundary conditions, where the nonlinearities D,S∈C2([0,∞)) are supposed to generalize the prototypes D(u)=CD(u+1)m−1andS(u)=CSu(u+1)q−1 with CD,CS>0 and m,q∈R, and f∈C1([0,∞)) satisfies f(u)≤r−buγ with r≥0,b>0 and γ>1. It is shown that if [Formula presented], then (⋆) has a unique globally bounded classical solution.

KW - Boundedness

KW - Chemotaxis

KW - Logistic source

KW - Quasilinear

UR - https://www.scopus.com/pages/publications/85019468888

U2 - 10.1016/j.nonrwa.2017.04.010

DO - 10.1016/j.nonrwa.2017.04.010

M3 - Article

AN - SCOPUS:85019468888

SN - 1468-1218

VL - 38

SP - 113

EP - 130

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

ER -

Boundedness in a quasilinear fully parabolic Keller–Segel system with logistic source

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Keywords

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