Global bounded solutions in a two-dimensional quasilinear Keller-Segel system with exponentially decaying diffusivity and subcritical sensitivity

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• 作者：Tomasz Cieślak^a ; ^{cieslak@impan.pl} ; Michael Winkler^b ; ^{michael.winkler@math.uni-paderborn.de}
• 关键词：Chemotaxis ; Degenerate diffusion ; Global existence ; Boundedness ; Moser iteration
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：June 2017
• 年：2017
• 卷：35
• 期：Complete
• 页码：1-19
• 全文大小：727 K
• 卷排序：35

文摘

The quasilinear chemotaxis system equation(∗∗){ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v),vt=Δv−v+u, is considered under homogeneous Neumann boundary conditions in a bounded domain Ω⊂R2Ω⊂R2 with smooth boundary.It is shown that if DD and SS are sufficiently smooth nonnegative functions on [0,∞)[0,∞) satisfying K1e−β−s≤D(s)≤K2e−β+sfor all s≥0 with some K1>0,K2>0K1>0,K2>0, β+>0β+>0 and β−≥β+β−≥β+, then whenever SS satisfies the condition of subcritical growth relative to DD given by S(s)D(s)≤K3sαfor all s≥0 with some K3>0K3>0 and α∈(0,1)α∈(0,1), for all suitably regular nonnegative initial data the corresponding initial–boundary value problem for (⋆⋆) possesses a global classical solution for which the component uu is bounded in Ω×(0,∞)Ω×(0,∞).