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- Title
Boundedness in a Quasilinear Chemotaxis Model with Logistic Growth and Indirect Signal Production.
- Authors
Wu, Sainan
- Abstract
This work considers the chemotaxis model with logistic growth and indirect signal production { u t = ∇ ⋅ (D (u) ∇ u) − ∇ ⋅ (u ∇ v) + f (u) , x ∈ Ω , t > 0 , v t = Δ v + w − v , x ∈ Ω , t > 0 , w t = Δ w + u − w , x ∈ Ω , t > 0 <graphic href="10440_2021_454_Article_Equa.gif"></graphic> under homogeneous Neumann boundary condition in a smooth bounded domain Ω ∈ R n (n ≥ 3 ). In this model, D and f are smooth functions satisfying D (u) ≥ D 1 u γ and f (u) ≤ μ (u − u α) with D 1 > 0 , γ ∈ R , α ≥ 2 and μ > 0 . Then if the assumption α n + γ 2 > 1 2 holds, the system possesses a classical solution which is global in time and bounded.
- Publication
Acta Applicandae Mathematicae, 2021, Vol 176, Issue 1, p1
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-021-00454-x