Existence and boundedness of solutions for a Keller-Segel system with gradient dependent chemotactic sensitivity
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Date
2020-12-16
Authors
Yan, Jianlu
Li, Yuxiang
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider the Keller-Segel system with gradient dependent chemotactic sensitivity
ut = Δu - ∇ ∙ (u|∇v|p-2∇v), x ∈ Ω, t > 0,
vt = Δv - v + u, x ∈ Ω, t > 0,
∂u/∂v = ∂ν/∂ν = 0, x ∈ ∂Ω, t > 0,
u(x, 0) = u0(x), v(x, 0) = v0(x), x ∈ Ω
in a smooth bounded domain Ω ⊂ ℝn, n ≥ 2. We shown that for all reasonably regular initial data u0 ≥ 0 and v0 ≥ 0, the corresponding Neumann initial-boundary value problem possesses a global weak solution which is uniformly bounded provided that 1 < p n/(n - 1).
Description
Keywords
Keller-Segel system, Weak solution, Chemotactic sensitivity
Citation
Yan, J., & Li, Y. (2020). Existence and boundedness of solutions for a Keller-Segel system with gradient dependent chemotactic sensitivity. <i>Electronic Journal of Differential Equations, 2020</i>(122), pp. 1-14.