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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.20675 |
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| _version_ | 1866908905010888704 |
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| author | Li, Shijun Zhao, Yashuang Xu, Shaopeng Li, Shengjun |
| author_facet | Li, Shijun Zhao, Yashuang Xu, Shaopeng Li, Shengjun |
| contents | We consider the Keller-Segel system with logical source \begin{align*} \begin{cases} u_t = \nabla \cdot (ϕ(u)\nabla u) - \nabla \cdot (ψ(u)\nabla v)+f(u), & x \in Ω, \; t > 0, v_t = Δv - v + u, & x \in Ω, \; t > 0, \end{cases} \end{align*} in a smooth bounded domain \(Ω\subset \mathbb{R}^n\) with \(n \geq 2\), the Neumann initial-boundary value problem admits a globally defined, uniformly bounded classic solution for all sufficiently regular non-negative initial data \(u_0\) and \(v_0\). In the first equation, assume that \(ϕ\) and \(ψ\) are dominated by a logarithmic function and a polynomial respectively. The logical source \(f\) representing the natural growth and decay of cells satisfies \(f \in W^{1,\infty}_{\mathrm{loc}}(Ω)\) and \(f(0) \geq 0\). Then we will see that the unique solution \(u \in C^{2,1}((\overlineΩ) \times [0,T] )\) and \(v \in W^{1,q}([0,T] ; C^{2,1}(\overlineΩ))\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20675 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Approximation Analysis of a Parabolic-Parabolic Chemotaxis Model with Logarithmic Nonlinearity Li, Shijun Zhao, Yashuang Xu, Shaopeng Li, Shengjun Analysis of PDEs We consider the Keller-Segel system with logical source \begin{align*} \begin{cases} u_t = \nabla \cdot (ϕ(u)\nabla u) - \nabla \cdot (ψ(u)\nabla v)+f(u), & x \in Ω, \; t > 0, v_t = Δv - v + u, & x \in Ω, \; t > 0, \end{cases} \end{align*} in a smooth bounded domain \(Ω\subset \mathbb{R}^n\) with \(n \geq 2\), the Neumann initial-boundary value problem admits a globally defined, uniformly bounded classic solution for all sufficiently regular non-negative initial data \(u_0\) and \(v_0\). In the first equation, assume that \(ϕ\) and \(ψ\) are dominated by a logarithmic function and a polynomial respectively. The logical source \(f\) representing the natural growth and decay of cells satisfies \(f \in W^{1,\infty}_{\mathrm{loc}}(Ω)\) and \(f(0) \geq 0\). Then we will see that the unique solution \(u \in C^{2,1}((\overlineΩ) \times [0,T] )\) and \(v \in W^{1,q}([0,T] ; C^{2,1}(\overlineΩ))\). |
| title | Approximation Analysis of a Parabolic-Parabolic Chemotaxis Model with Logarithmic Nonlinearity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.20675 |