Details
| Original language | English |
|---|---|
| Pages (from-to) | 14362-14378 |
| Number of pages | 17 |
| Journal | Mathematical Methods in the Applied Sciences |
| Volume | 46 |
| Issue number | 13 |
| Publication status | Published - 15 Aug 2023 |
Abstract
In this paper, we deal with quasilinear Keller–Segel systems with indirect signal production, (Figure presented.) complemented with homogeneous Neumann boundary conditions and suitable initial conditions, where (Figure presented.) (Figure presented.) is a bounded smooth domain, (Figure presented.) and (Figure presented.) We show that in the case (Figure presented.), there exists (Figure presented.) such that if either (Figure presented.) or (Figure presented.), then the solution exists globally and remains bounded, and that in the case (Figure presented.), if either (Figure presented.) or (Figure presented.), then there exist radially symmetric initial data such that (Figure presented.) and the solution blows up in finite or infinite time, where the blow-up time is infinite if (Figure presented.). In particular, if (Figure presented.), there is a critical mass phenomenon in the sense that (Figure presented.) is a finite positive number.
Keywords
- chemotaxis, indirect signal production, infinite-time blow-up
ASJC Scopus subject areas
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In: Mathematical Methods in the Applied Sciences, Vol. 46, No. 13, 15.08.2023, p. 14362-14378.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Critical mass phenomena in higher dimensional quasilinear Keller–Segel systems with indirect signal production
AU - Fuest, Mario
AU - Lankeit, Johannes
AU - Tanaka, Yuya
N1 - Funding Information: The third author is supported by JSPS KAKENHI Grant Number JP22J11193. Open Access funding enabled and organized by Projekt DEAL.
PY - 2023/8/15
Y1 - 2023/8/15
N2 - In this paper, we deal with quasilinear Keller–Segel systems with indirect signal production, (Figure presented.) complemented with homogeneous Neumann boundary conditions and suitable initial conditions, where (Figure presented.) (Figure presented.) is a bounded smooth domain, (Figure presented.) and (Figure presented.) We show that in the case (Figure presented.), there exists (Figure presented.) such that if either (Figure presented.) or (Figure presented.), then the solution exists globally and remains bounded, and that in the case (Figure presented.), if either (Figure presented.) or (Figure presented.), then there exist radially symmetric initial data such that (Figure presented.) and the solution blows up in finite or infinite time, where the blow-up time is infinite if (Figure presented.). In particular, if (Figure presented.), there is a critical mass phenomenon in the sense that (Figure presented.) is a finite positive number.
AB - In this paper, we deal with quasilinear Keller–Segel systems with indirect signal production, (Figure presented.) complemented with homogeneous Neumann boundary conditions and suitable initial conditions, where (Figure presented.) (Figure presented.) is a bounded smooth domain, (Figure presented.) and (Figure presented.) We show that in the case (Figure presented.), there exists (Figure presented.) such that if either (Figure presented.) or (Figure presented.), then the solution exists globally and remains bounded, and that in the case (Figure presented.), if either (Figure presented.) or (Figure presented.), then there exist radially symmetric initial data such that (Figure presented.) and the solution blows up in finite or infinite time, where the blow-up time is infinite if (Figure presented.). In particular, if (Figure presented.), there is a critical mass phenomenon in the sense that (Figure presented.) is a finite positive number.
KW - chemotaxis
KW - indirect signal production
KW - infinite-time blow-up
UR - http://www.scopus.com/inward/record.url?scp=85158138542&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2302.00996
DO - 10.48550/arXiv.2302.00996
M3 - Article
AN - SCOPUS:85158138542
VL - 46
SP - 14362
EP - 14378
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
SN - 0170-4214
IS - 13
ER -