On Asymptotically Almost Periodic Solutions of the parabolic-elliptic Keller-Segel system on real hyperbolic Manifolds
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929356576653312 |
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| author | Xuan, Pham Truong Van Thuy, Tran Van, Nguyen Thi |
| author_facet | Xuan, Pham Truong Van Thuy, Tran Van, Nguyen Thi |
| contents | In this article we investigate the existence, uniqueness and exponential decay of asymptotically almost periodic solutions of the parabolic-elliptic Keller-Segel system on a real hyperbolic manifold. We prove the existence and uniqueness of such solutions in the linear equation case by using the dispersive and smoothing estimates of the heat semigroup. Then we pass to the well-posedness of semi-linear equation case by using the results of linear equation and fixed point arguments. The exponential decay is proven by using Gronwall's inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06492 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Asymptotically Almost Periodic Solutions of the parabolic-elliptic Keller-Segel system on real hyperbolic Manifolds Xuan, Pham Truong Van Thuy, Tran Van, Nguyen Thi Analysis of PDEs Mathematical Physics Dynamical Systems Functional Analysis In this article we investigate the existence, uniqueness and exponential decay of asymptotically almost periodic solutions of the parabolic-elliptic Keller-Segel system on a real hyperbolic manifold. We prove the existence and uniqueness of such solutions in the linear equation case by using the dispersive and smoothing estimates of the heat semigroup. Then we pass to the well-posedness of semi-linear equation case by using the results of linear equation and fixed point arguments. The exponential decay is proven by using Gronwall's inequality. |
| title | On Asymptotically Almost Periodic Solutions of the parabolic-elliptic Keller-Segel system on real hyperbolic Manifolds |
| topic | Analysis of PDEs Mathematical Physics Dynamical Systems Functional Analysis |
| url | https://arxiv.org/abs/2403.06492 |