Details
| Original language | English |
|---|---|
| Pages (from-to) | 4052-4084 |
| Number of pages | 33 |
| Journal | Journal of differential equations |
| Volume | 262 |
| Issue number | 7 |
| Publication status | Published - 2017 |
Abstract
We show the existence of locally bounded global solutions to the chemotaxis system {u t=∇⋅(D(u)∇u)−∇⋅([formula presented]∇v)in Ω×(0,∞)v t=Δv−uvin Ω×(0,∞)∂ νu=∂ νv=0in ∂Ω×(0,∞)u(⋅,0)=u 0,v(⋅,0)=v 0in Ω in smooth bounded domains Ω⊂R N, N≥2, for D(u)≥δu m−1 with some δ>0, provided that m>1+[formula presented].
Keywords
- Boundedness, Chemotaxis, Global existence, Keller–Segel, Nonlinear diffusion
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Journal of differential equations, Vol. 262, No. 7, 2017, p. 4052-4084.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion
AU - Lankeit, J.
N1 - Publisher Copyright: © 2016 Elsevier Inc.
PY - 2017
Y1 - 2017
N2 - We show the existence of locally bounded global solutions to the chemotaxis system {u t=∇⋅(D(u)∇u)−∇⋅([formula presented]∇v)in Ω×(0,∞)v t=Δv−uvin Ω×(0,∞)∂ νu=∂ νv=0in ∂Ω×(0,∞)u(⋅,0)=u 0,v(⋅,0)=v 0in Ω in smooth bounded domains Ω⊂R N, N≥2, for D(u)≥δu m−1 with some δ>0, provided that m>1+[formula presented].
AB - We show the existence of locally bounded global solutions to the chemotaxis system {u t=∇⋅(D(u)∇u)−∇⋅([formula presented]∇v)in Ω×(0,∞)v t=Δv−uvin Ω×(0,∞)∂ νu=∂ νv=0in ∂Ω×(0,∞)u(⋅,0)=u 0,v(⋅,0)=v 0in Ω in smooth bounded domains Ω⊂R N, N≥2, for D(u)≥δu m−1 with some δ>0, provided that m>1+[formula presented].
KW - Boundedness
KW - Chemotaxis
KW - Global existence
KW - Keller–Segel
KW - Nonlinear diffusion
UR - http://www.scopus.com/inward/record.url?scp=85008225418&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2016.12.007
DO - 10.1016/j.jde.2016.12.007
M3 - Article
VL - 262
SP - 4052
EP - 4084
JO - Journal of differential equations
JF - Journal of differential equations
SN - 0022-0396
IS - 7
ER -