Details
| Original language | English |
|---|---|
| Pages (from-to) | 49-65 |
| Number of pages | 17 |
| Journal | Zeitschrift für Analysis und ihre Anwendungen |
| Volume | 43 |
| Issue number | 1/2 |
| Publication status | Published - 20 Mar 2024 |
Abstract
In this paper, we give sufficient conditions for global-in-time existence of classical solutions for the fully parabolic chemorepulsion system posed on a convex, bounded three-dimensional domain. Our main result establishes global-in-time existence of regular nonnegative solutions provided that ∇√u ∊ L4(0, T; L2(Ω)). Our method is related to the Bakry–Émery calculation and appears to be new in this context.
Keywords
- Bernis-type inequality, boundedness of solutions, chemorepulsion, chemotaxis, Lyapunov-like functional
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Zeitschrift für Analysis und ihre Anwendungen, Vol. 43, No. 1/2, 20.03.2024, p. 49-65.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the existence of global solutions for the 3D chemorepulsion system
AU - Cieślak, Tomasz
AU - Fuest, Mario
AU - Hajduk, Karol
AU - Sierzęga, Mikołaj
N1 - Publisher Copyright: © 2024 European Mathematical Society.
PY - 2024/3/20
Y1 - 2024/3/20
N2 - In this paper, we give sufficient conditions for global-in-time existence of classical solutions for the fully parabolic chemorepulsion system posed on a convex, bounded three-dimensional domain. Our main result establishes global-in-time existence of regular nonnegative solutions provided that ∇√u ∊ L4(0, T; L2(Ω)). Our method is related to the Bakry–Émery calculation and appears to be new in this context.
AB - In this paper, we give sufficient conditions for global-in-time existence of classical solutions for the fully parabolic chemorepulsion system posed on a convex, bounded three-dimensional domain. Our main result establishes global-in-time existence of regular nonnegative solutions provided that ∇√u ∊ L4(0, T; L2(Ω)). Our method is related to the Bakry–Émery calculation and appears to be new in this context.
KW - Bernis-type inequality
KW - boundedness of solutions
KW - chemorepulsion
KW - chemotaxis
KW - Lyapunov-like functional
UR - http://www.scopus.com/inward/record.url?scp=85192157439&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2303.09620
DO - 10.48550/arXiv.2303.09620
M3 - Article
AN - SCOPUS:85192157439
VL - 43
SP - 49
EP - 65
JO - Zeitschrift für Analysis und ihre Anwendungen
JF - Zeitschrift für Analysis und ihre Anwendungen
SN - 0232-2064
IS - 1/2
ER -