TY - JOUR
T1 - A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system
AU - Fujie, Kentarou
AU - Senba, Takasi
N1 - Funding Information:
3 The second author was partially supported by the Japan Society for the Promotion of Science: Grant-in-Aid for Scientific Research (C) (No. 26400172).
Publisher Copyright:
© 2018 IOP Publishing Ltd & London Mathematical Society.
PY - 2018/3/12
Y1 - 2018/3/12
N2 - This paper deals with time-global solutions to the parabolic system {τut = Δu - ∇ · (u∇ χ (ν)) in Ω × (0, ∞), νt = Δν - ν + u in Ω × (0,∞), under the homogeneous Neumann boundary conditions in a bounded and convex domain Ω ⊂ ℝn (n ≥ 2) with smooth boundary ∂Ω. Here τ is a positive parameter, χ is a smooth function on (0,∞) satisfying χ' > 0 and (u0, ν0) is a pair of nonnegative initial data. We will consider the above system as a perturbation of a nonlocal parabolic equation and establish a sufficient condition of the sensitivity function ? for the global existence of solutions under the assumption of smallness of the constant τ.
AB - This paper deals with time-global solutions to the parabolic system {τut = Δu - ∇ · (u∇ χ (ν)) in Ω × (0, ∞), νt = Δν - ν + u in Ω × (0,∞), under the homogeneous Neumann boundary conditions in a bounded and convex domain Ω ⊂ ℝn (n ≥ 2) with smooth boundary ∂Ω. Here τ is a positive parameter, χ is a smooth function on (0,∞) satisfying χ' > 0 and (u0, ν0) is a pair of nonnegative initial data. We will consider the above system as a perturbation of a nonlocal parabolic equation and establish a sufficient condition of the sensitivity function ? for the global existence of solutions under the assumption of smallness of the constant τ.
KW - chemotaxis
KW - sensitivity function
KW - time-global existence
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U2 - 10.1088/1361-6544/aaa2df
DO - 10.1088/1361-6544/aaa2df
M3 - Article
AN - SCOPUS:85045233192
VL - 31
SP - 1639
EP - 1672
JO - Nonlinearity
JF - Nonlinearity
SN - 0951-7715
IS - 4
ER -