趋化系统解的全局存在性与有界性——献给陈化教授 70 寿辰

Abstract

Abstract:

This paper is concerned with the global existence for a class of Keller-Segel model $$\begin{equation*} \begin{cases} u_t=\Delta(\gamma (v)u)+\rho u-\mu u^\alpha,&x\in\Omega,\,t>0,\\ v_t=\Delta v-v+u^\beta,&x\in\Omega,\,t>0, \end{cases} \end{equation*}$$ under homogeneous Neumann boundary conditions in a smoothly bounded domain $\Omega\subset\mathbb{R}^n\,(n\geqslant1)$. It is proved that for $\rho\in\mathbb{R},\,\mu>0$, $\alpha> 1$, $\beta>0$ satisfying certain additional relations, and under suitable assumptions on the motility function $\gamma$, the system admits a global classical solution for all sufficiently smooth initial data. This result improves recent ones established in [Lv W B, Wang Q Y. Proc Roy Soc Edinburgh, 2021, 151(2): 821-841], [Tao X Y, Fang Z B. Z Angew Math Phys, 2022, 73(3): Art 123].

Key words: global existence, chemotaxis, boundedness, general logistic source

CLC Number:

O175.23

Yaping Guo, Jialin Li, Wenbin Lyu. Global Existence for a Class of Chemotaxis Systems with Signal-Dependent Motility and Generalized Logistic Source[J].Acta mathematica scientia,Series A, 2026, 46(2): 535-551.

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References 49

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Global Existence for a Class of Chemotaxis Systems with Signal-Dependent Motility and Generalized Logistic Source

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