On the existence of solutions for a parabolic-elliptic chemotaxis model with flux limitation and logistic source
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913501728997376 |
|---|---|
| author | Sastre-Gomez, Silvia Tello, J. Ignacio |
| author_facet | Sastre-Gomez, Silvia Tello, J. Ignacio |
| contents | In this paper we study the existence of solutions of a parabolic-elliptic system of partial differential equations describing the behaviour of a biological species $u$ and a chemical stimulus $v$ in a bounded and regular domain $Ω$ of $\mathbb{R}^N$. The equation for $u$ is a parabolic equation with a nonlinear second order term of chemotaxis type with flux limitation as $ -χdiv (u |\nabla ψ|^{p-2} \nabla v)$, for $p>1$. The chemical substance distribution $v$ satisfies the elliptic equation $-Δv+v=u$. The evolution of $u$ is also determined by a logistic type growth term $μu(1-u)$. The system is studied under homogeneous Neumann boundary conditions. The main result of the article is the existence of uniformly bounded solutions for $p<3/2$ and any $N\ge 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the existence of solutions for a parabolic-elliptic chemotaxis model with flux limitation and logistic source Sastre-Gomez, Silvia Tello, J. Ignacio Analysis of PDEs In this paper we study the existence of solutions of a parabolic-elliptic system of partial differential equations describing the behaviour of a biological species $u$ and a chemical stimulus $v$ in a bounded and regular domain $Ω$ of $\mathbb{R}^N$. The equation for $u$ is a parabolic equation with a nonlinear second order term of chemotaxis type with flux limitation as $ -χdiv (u |\nabla ψ|^{p-2} \nabla v)$, for $p>1$. The chemical substance distribution $v$ satisfies the elliptic equation $-Δv+v=u$. The evolution of $u$ is also determined by a logistic type growth term $μu(1-u)$. The system is studied under homogeneous Neumann boundary conditions. The main result of the article is the existence of uniformly bounded solutions for $p<3/2$ and any $N\ge 2$. |
| title | On the existence of solutions for a parabolic-elliptic chemotaxis model with flux limitation and logistic source |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.10121 |