Details
| Original language | English |
|---|---|
| Pages (from-to) | 394-404 |
| Number of pages | 11 |
| Journal | Mathematical Methods in the Applied Sciences |
| Volume | 39 |
| Issue number | 3 |
| Early online date | 16 Apr 2015 |
| Publication status | Published - 1 Feb 2016 |
| Externally published | Yes |
Abstract
We consider the parabolic chemotaxis model ut=Δu-χ∇·uv∇vvt=Δv-v+u in a smooth, bounded, convex two-dimensional domain and show global existence and boundedness of solutions for χ∈(0,χ0) for some χ0>1, thereby proving that the value χ = 1 is not critical in this regard. Our main tool is consideration of the energy functional Fa,b(u,v)=∫Ωulnu-a∫Ωulnv+b∫Ω∇v2 for a > 0, b≥0, where using nonzero values of b appears to be new in this context.
Keywords
- boundedness, chemotaxis, global existence, singular sensitivity
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Engineering(all)
- General Engineering
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In: Mathematical Methods in the Applied Sciences, Vol. 39, No. 3, 01.02.2016, p. 394-404.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity
AU - Lankeit, Johannes
PY - 2016/2/1
Y1 - 2016/2/1
N2 - We consider the parabolic chemotaxis model ut=Δu-χ∇·uv∇vvt=Δv-v+u in a smooth, bounded, convex two-dimensional domain and show global existence and boundedness of solutions for χ∈(0,χ0) for some χ0>1, thereby proving that the value χ = 1 is not critical in this regard. Our main tool is consideration of the energy functional Fa,b(u,v)=∫Ωulnu-a∫Ωulnv+b∫Ω∇v2 for a > 0, b≥0, where using nonzero values of b appears to be new in this context.
AB - We consider the parabolic chemotaxis model ut=Δu-χ∇·uv∇vvt=Δv-v+u in a smooth, bounded, convex two-dimensional domain and show global existence and boundedness of solutions for χ∈(0,χ0) for some χ0>1, thereby proving that the value χ = 1 is not critical in this regard. Our main tool is consideration of the energy functional Fa,b(u,v)=∫Ωulnu-a∫Ωulnv+b∫Ω∇v2 for a > 0, b≥0, where using nonzero values of b appears to be new in this context.
KW - boundedness
KW - chemotaxis
KW - global existence
KW - singular sensitivity
UR - http://www.scopus.com/inward/record.url?scp=84956951920&partnerID=8YFLogxK
U2 - 10.1002/mma.3489
DO - 10.1002/mma.3489
M3 - Article
AN - SCOPUS:84956951920
VL - 39
SP - 394
EP - 404
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
SN - 0170-4214
IS - 3
ER -