On pseudo almost Periodic Solutions of the parabolic-elliptic Keller-Segel systems
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908402653855744 |
|---|---|
| author | Xuan, Pham Truong Van, Nguyen Thi Nguyet, Tran Minh Loan, Nguyen Thi |
| author_facet | Xuan, Pham Truong Van, Nguyen Thi Nguyet, Tran Minh Loan, Nguyen Thi |
| contents | In this paper we investigate the existence, uniqueness and exponential stability of pseudo almost periodic (PAP-) mild solutions of the parabolic-elliptic (P-E) Keller-Segel system on a bounded domain $Ω\in \mathbb{R}^n$ with smooth boundary. First, the well-posedness of the corresponding linear system is established by using the smoothing estimates of the Neumann heat semigroup on $Ω$. Then, the existence of PAP-mild solution of linear system is done by proving a Massera-type principle. Next, we obtain the well-posedness of such solutions for semilinear system by using the results of linear system and fixed point arguments. The exponential stability is proven by using again the estimates of the Neumann heat semigroup. Finally, we discuss also such results for the case of the Keller-Segel system on the framework of real hyperbolic manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06341 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On pseudo almost Periodic Solutions of the parabolic-elliptic Keller-Segel systems Xuan, Pham Truong Van, Nguyen Thi Nguyet, Tran Minh Loan, Nguyen Thi Analysis of PDEs In this paper we investigate the existence, uniqueness and exponential stability of pseudo almost periodic (PAP-) mild solutions of the parabolic-elliptic (P-E) Keller-Segel system on a bounded domain $Ω\in \mathbb{R}^n$ with smooth boundary. First, the well-posedness of the corresponding linear system is established by using the smoothing estimates of the Neumann heat semigroup on $Ω$. Then, the existence of PAP-mild solution of linear system is done by proving a Massera-type principle. Next, we obtain the well-posedness of such solutions for semilinear system by using the results of linear system and fixed point arguments. The exponential stability is proven by using again the estimates of the Neumann heat semigroup. Finally, we discuss also such results for the case of the Keller-Segel system on the framework of real hyperbolic manifolds. |
| title | On pseudo almost Periodic Solutions of the parabolic-elliptic Keller-Segel systems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.06341 |