TY - JOUR
T1 - Boundedness in a quasilinear fully parabolic Keller–Segel system with logistic source
AU - Wang, Yifu
AU - Liu, Ji
N1 - Publisher Copyright:
© 2017 Elsevier Ltd
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 - http://www.scopus.com/inward/record.url?scp=85019468888&partnerID=8YFLogxK
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 -