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- Title
Periodic solutions of the parabolic–elliptic Keller–Segel system on whole spaces.
- Authors
Loan, Nguyen Thi; Nguyen Thi, Van Anh; Van Thuy, Tran; Xuan, Pham Truong
- Abstract
In this paper, we investigate to the existence and uniqueness of periodic solutions for the parabolic–elliptic Keller–Segel system on whole spaces detailized by Euclidean space Rn(wheren⩾4)$\mathbb {R}^n\,\,(\hbox{ where }n \geqslant 4)$ and real hyperbolic space Hn(wheren⩾2)$\mathbb {H}^n\,\, (\hbox{where }n \geqslant 2)$. We work in framework of critical spaces such as on weak‐Lorentz space Ln2,∞(Rn)$L^{\frac{n}{2},\infty }(\mathbb {R}^n)$ to obtain the results for the Keller–Segel system on Rn$\mathbb {R}^n$ and on Lp2(Hn)$L^{\frac{p}{2}}(\mathbb {H}^n)$ for n<p<2n$n<p<2n$ to obtain those on Hn$\mathbb {H}^n$. Our method is based on the dispersive and smoothing estimates of the heat semigroup and fixed point arguments. This work provides also a fully comparison between the asymptotic behaviors of periodic mild solutions of the Keller–Segel system obtained in Rn$\mathbb {R}^n$ and the one in Hn$\mathbb {H}^n$.
- Subjects
EXPONENTIAL stability; POLYNOMIALS; ARGUMENT
- Publication
Mathematische Nachrichten, 2024, Vol 297, Issue 8, p3003
- ISSN
0025-584X
- Publication type
Article
- DOI
10.1002/mana.202300311