Details
| Original language | English |
|---|---|
| Article number | 49 |
| Number of pages | 33 |
| Journal | Nonlinear Differential Equations and Applications |
| Volume | 24 |
| Publication status | Published - 20 Jul 2017 |
| Externally published | Yes |
Abstract
The chemotaxis system (Formula presented.) is considered in a bounded domain Ω ⊂ Rn with smooth boundary, where χ> 0. An apparently novel type of generalized solution framework is introduced within which an extension of previously known ranges for the key parameter χ with regard to global solvability is achieved. In particular, it is shown that under the hypothesis that (Formula presented.) for all initial data satisfying suitable assumptions on regularity and positivity, an associated no-flux initial-boundary value problem admits a globally defined generalized solution. This solution inter alia has the property that (Formula presented.).
Keywords
- Chemotaxis, Generalized solution, Global existence, Logarithmic sensitivity
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Nonlinear Differential Equations and Applications, Vol. 24, 49, 20.07.2017.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A generalized solution concept for the Keller–Segel system with logarithmic sensitivity
T2 - global solvability for large nonradial data
AU - Lankeit, Johannes
AU - Winkler, Michael
PY - 2017/7/20
Y1 - 2017/7/20
N2 - The chemotaxis system (Formula presented.) is considered in a bounded domain Ω ⊂ Rn with smooth boundary, where χ> 0. An apparently novel type of generalized solution framework is introduced within which an extension of previously known ranges for the key parameter χ with regard to global solvability is achieved. In particular, it is shown that under the hypothesis that (Formula presented.) for all initial data satisfying suitable assumptions on regularity and positivity, an associated no-flux initial-boundary value problem admits a globally defined generalized solution. This solution inter alia has the property that (Formula presented.).
AB - The chemotaxis system (Formula presented.) is considered in a bounded domain Ω ⊂ Rn with smooth boundary, where χ> 0. An apparently novel type of generalized solution framework is introduced within which an extension of previously known ranges for the key parameter χ with regard to global solvability is achieved. In particular, it is shown that under the hypothesis that (Formula presented.) for all initial data satisfying suitable assumptions on regularity and positivity, an associated no-flux initial-boundary value problem admits a globally defined generalized solution. This solution inter alia has the property that (Formula presented.).
KW - Chemotaxis
KW - Generalized solution
KW - Global existence
KW - Logarithmic sensitivity
UR - http://www.scopus.com/inward/record.url?scp=85025106709&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1701.07391
DO - 10.48550/arXiv.1701.07391
M3 - Article
AN - SCOPUS:85025106709
VL - 24
JO - Nonlinear Differential Equations and Applications
JF - Nonlinear Differential Equations and Applications
SN - 1021-9722
M1 - 49
ER -