Details
| Original language | English |
|---|---|
| Pages (from-to) | 3515-3534 |
| Number of pages | 20 |
| Journal | Applicable analysis |
| Volume | 101 |
| Issue number | 9 |
| Early online date | 2 Dec 2020 |
| Publication status | Published - 13 Jun 2022 |
| Externally published | Yes |
Abstract
Solutions (Formula presented.) to the chemotaxis system (Formula presented.) in a ball (Formula presented.), (Formula presented.), wherein (Formula presented.) and (Formula presented.) are given parameters with m−q>−1, cannot blow up in finite time provided u is uniformly-in-time bounded in (Formula presented.) for some (Formula presented.). For radially symmetric solutions, we show that, if u is only bounded in (Formula presented.) and the technical condition (Formula presented.) is fulfilled, then, for any (Formula presented.), there is C>0 with (Formula presented.) (Formula presented.) denoting the maximal existence time. This is essentially optimal in the sense that, if this estimate held for any (Formula presented.), then u would already be bounded in (Formula presented.) for some (Formula presented.).
Keywords
- 35K65, 92C17, Blow-up profile, Primary: 35B40, Secondary: 35K40, chemotaxis, gradient estimates, nonlinear diffusion
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Applicable analysis, Vol. 101, No. 9, 13.06.2022, p. 3515-3534.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the optimality of upper estimates near blow-up in quasilinear Keller–Segel systems
AU - Fuest, Mario
N1 - Publisher Copyright: © 2020 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2022/6/13
Y1 - 2022/6/13
N2 - Solutions (Formula presented.) to the chemotaxis system (Formula presented.) in a ball (Formula presented.), (Formula presented.), wherein (Formula presented.) and (Formula presented.) are given parameters with m−q>−1, cannot blow up in finite time provided u is uniformly-in-time bounded in (Formula presented.) for some (Formula presented.). For radially symmetric solutions, we show that, if u is only bounded in (Formula presented.) and the technical condition (Formula presented.) is fulfilled, then, for any (Formula presented.), there is C>0 with (Formula presented.) (Formula presented.) denoting the maximal existence time. This is essentially optimal in the sense that, if this estimate held for any (Formula presented.), then u would already be bounded in (Formula presented.) for some (Formula presented.).
AB - Solutions (Formula presented.) to the chemotaxis system (Formula presented.) in a ball (Formula presented.), (Formula presented.), wherein (Formula presented.) and (Formula presented.) are given parameters with m−q>−1, cannot blow up in finite time provided u is uniformly-in-time bounded in (Formula presented.) for some (Formula presented.). For radially symmetric solutions, we show that, if u is only bounded in (Formula presented.) and the technical condition (Formula presented.) is fulfilled, then, for any (Formula presented.), there is C>0 with (Formula presented.) (Formula presented.) denoting the maximal existence time. This is essentially optimal in the sense that, if this estimate held for any (Formula presented.), then u would already be bounded in (Formula presented.) for some (Formula presented.).
KW - 35K65
KW - 92C17
KW - Blow-up profile
KW - Primary: 35B40
KW - Secondary: 35K40
KW - chemotaxis
KW - gradient estimates
KW - nonlinear diffusion
UR - http://www.scopus.com/inward/record.url?scp=85096985672&partnerID=8YFLogxK
U2 - 10.1080/00036811.2020.1854234
DO - 10.1080/00036811.2020.1854234
M3 - Article
VL - 101
SP - 3515
EP - 3534
JO - Applicable analysis
JF - Applicable analysis
SN - 0003-6811
IS - 9
ER -