Details
| Original language | English |
|---|---|
| Pages (from-to) | 1158-1191 |
| Number of pages | 34 |
| Journal | Journal of differential equations |
| Volume | 258 |
| Issue number | 4 |
| Publication status | Published - 15 Feb 2015 |
| Externally published | Yes |
Abstract
We prove existence of global weak solutions to the chemotaxis system. u t=δu-{dot operator}(u;v)+κu-μu 2 v t=δv-v+u under homogeneous Neumann boundary conditions in a smooth bounded convex domain Ω⊂R n, for arbitrarily small values of μ. >. 0.Additionally, we show that in the three-dimensional setting, after some time, these solutions become classical solutions, provided that κ is not too large. In this case, we also consider their large-time behaviour: We prove decay if κ. ≤. 0 and the existence of an absorbing set if κ. >. 0 is sufficiently small.
Keywords
- Chemotaxis, Eventual smoothness, Existence, Logistic source, Primary, Secondary, Weak solutions
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Journal of differential equations, Vol. 258, No. 4, 15.02.2015, p. 1158-1191.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source
AU - Lankeit, Johannes
N1 - Publisher Copyright: © 2014 Elsevier Inc.
PY - 2015/2/15
Y1 - 2015/2/15
N2 - We prove existence of global weak solutions to the chemotaxis system. u t=δu-{dot operator}(u;v)+κu-μu 2 v t=δv-v+u under homogeneous Neumann boundary conditions in a smooth bounded convex domain Ω⊂R n, for arbitrarily small values of μ. >. 0.Additionally, we show that in the three-dimensional setting, after some time, these solutions become classical solutions, provided that κ is not too large. In this case, we also consider their large-time behaviour: We prove decay if κ. ≤. 0 and the existence of an absorbing set if κ. >. 0 is sufficiently small.
AB - We prove existence of global weak solutions to the chemotaxis system. u t=δu-{dot operator}(u;v)+κu-μu 2 v t=δv-v+u under homogeneous Neumann boundary conditions in a smooth bounded convex domain Ω⊂R n, for arbitrarily small values of μ. >. 0.Additionally, we show that in the three-dimensional setting, after some time, these solutions become classical solutions, provided that κ is not too large. In this case, we also consider their large-time behaviour: We prove decay if κ. ≤. 0 and the existence of an absorbing set if κ. >. 0 is sufficiently small.
KW - Chemotaxis
KW - Eventual smoothness
KW - Existence
KW - Logistic source
KW - Primary
KW - Secondary
KW - Weak solutions
UR - http://www.scopus.com/inward/record.url?scp=84920767635&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2014.10.016
DO - 10.1016/j.jde.2014.10.016
M3 - Article
VL - 258
SP - 1158
EP - 1191
JO - Journal of differential equations
JF - Journal of differential equations
SN - 0022-0396
IS - 4
ER -