Periodic Solutions of the parabolic-elliptic Keller-Segel system on whole spaces
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909183284084736 |
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| author | Xuan, Pham Truong Van Thuy, Tran Van Anh, Nguyen Thi Loan, Nguyen Thi |
| author_facet | Xuan, Pham Truong Van Thuy, Tran Van Anh, Nguyen Thi Loan, Nguyen Thi |
| contents | 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 $\mathbb{R}^n\,\,(\hbox{ where }n \geqslant 4)$ and real hyperbolic space $\mathbb{H}^n\,\, (\hbox{where }n \geqslant 2)$. We work in framework of scritical spaces such as on weak-Lorentz space $L^{\frac{n}{2},\infty}(\mathbb{R}^n)$ to obtain the results for Keller-Segel system on $\mathbb{R}^n$ and on $L^{\frac{p}{2}}(\mathbb{H}^n)$ for $n<p<2n$ to obtain the ones on $\mathbb{H}^n$. 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 behaviours of periodic mild solutions of Keller-Segel system obtained in $\mathbb{R}^n$ and the one in $\mathbb{H}^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_05681 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Periodic Solutions of the parabolic-elliptic Keller-Segel system on whole spaces Xuan, Pham Truong Van Thuy, Tran Van Anh, Nguyen Thi Loan, Nguyen Thi Analysis of PDEs Differential Geometry Dynamical Systems Functional Analysis 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 $\mathbb{R}^n\,\,(\hbox{ where }n \geqslant 4)$ and real hyperbolic space $\mathbb{H}^n\,\, (\hbox{where }n \geqslant 2)$. We work in framework of scritical spaces such as on weak-Lorentz space $L^{\frac{n}{2},\infty}(\mathbb{R}^n)$ to obtain the results for Keller-Segel system on $\mathbb{R}^n$ and on $L^{\frac{p}{2}}(\mathbb{H}^n)$ for $n<p<2n$ to obtain the ones on $\mathbb{H}^n$. 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 behaviours of periodic mild solutions of Keller-Segel system obtained in $\mathbb{R}^n$ and the one in $\mathbb{H}^n$. |
| title | Periodic Solutions of the parabolic-elliptic Keller-Segel system on whole spaces |
| topic | Analysis of PDEs Differential Geometry Dynamical Systems Functional Analysis |
| url | https://arxiv.org/abs/2304.05681 |