This paper is devoted to the chemotaxis model with indirect production and general kinetic function

in a bounded domain \(\Omega \subset \mathbb {R}^n(n\le 3)\) with smooth boundary \(\partial \Omega \), where \(\chi , \tau , \lambda \) are given positive parameters, f and g are known functions. We find several explicit conditions involving the kinetic function f, g, the parameters \(\chi \), \(\lambda \), and the initial data \(\Vert u_0\Vert _{L^1(\Omega )}\) to ensure the global-in-time existence and uniform boundedness for the corresponding 2D/3D Neumann initial-boundary value problem. Particularly, when \(f\equiv 0\), and g is a linear function, the global bounded classical solutions to the corresponding 2D Neumann initial-boundary value problem with arbitrarily large initial data and chemotactic sensitivity are established. Our results partially extend the results of Hu and Tao (Math Models Methods Appl Sci 26:2111–2128, 2016), Tao and Winkler (J Eur Math Soc 19:3641–3678, 2017), etc.

本文致力于具有间接产生和一般动力学功能的趋化模型

在具有平滑边界\（\ partial \ Omega \）的有界域\（\ Omega \ subset \ mathbb {R} ^ n（n \ le 3）\）中，其中\（\ chi，\ tau，\ lambda \）给定正参数，f和g是已知函数。我们发现了几个明确的条件，其中包括动力学函数f，g，参数\（\ chi \），\（\ lambda \）和初始数据\（\ Vert u_0 \ Vert _ {L ^ 1（\ Omega）} \）确保相应的2D / 3D诺伊曼初始边界值问题的全局及时存在性和一致有界性。特别是当\（f \ equiv 0 \）和g是一个线性函数，建立了具有任意大初始数据和趋化敏感性的相应2D Neumann初值问题的全局有界经典解。我们的结果部分扩展了Hu和Tao（Math Models Methods Appl Sci 26：2111–2128，2016），Tao和Winkler（J Eur Math Soc 19：3641–3678，2017）等的结果。