Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion

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• 作者：Johannes Lankeit ^{johannes.lankeit@math.uni-paderborn.de}
• 关键词：35K55 ; 35A01 ; 35K65 ; 92C17
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 April 2017
• 年：2017
• 卷：262
• 期：7
• 页码：4052-4084
• 全文大小：487 K
• 卷排序：262

文摘

We show the existence of locally bounded global solutions to the chemotaxis system{ut=∇⋅(D(u)∇u)−∇⋅(uv∇v)in Ω×(0,∞)vt=Δv−uvin Ω×(0,∞)∂νu=∂νv=0in ∂Ω×(0,∞)u(⋅,0)=u0,v(⋅,0)=v0in Ω in smooth bounded domains Ω⊂RNΩ⊂RN, N≥2N≥2, for D(u)≥δum−1D(u)≥δum−1 with some δ>0δ>0, provided that m>1+N4.