This paper deals with a parabolic–elliptic chemotaxis-consumption system with tensor-valued sensitivity $S(x,n,c)$ under no-flux boundary conditions for $n$ and Robin-type boundary conditions for $c$. The global existence of bounded classical solutions is established in dimension two under general assumptions on tensor-valued sensitivity $S$. One of the main steps is to show that $\nabla c(\cdot ,t)$ becomes tiny in $L^2(B_r(x)\cap \mathrm{\Omega })$ for every $x\in \overline{\mathrm{\Omega }}$ and $t$ when $r$ is sufficiently small, which seems to be of independent interest. On the other hand, in the case of scalar-valued sensitivity $S=\chi (x,n,c)𝕀$, there exists a bounded classical solution globally in time for two and higher dimensions provided the domain is a ball with radius $R$ and all given data are radial. The result of the radial case covers scalar-valued sensitivity $\chi$ that can be singular at $c=0$.

本文讨论具有张量值灵敏度的抛物线-椭圆趋化消耗系统$S（X,n,C）$在无通量边界条件下$n$和 Robin 型边界条件$C$。在张量值敏感性的一般假设下，在第二维中建立了有界经典解的全局存在性$S$。主要步骤之一是证明$\nabla C（\cdot ,t）$变得很小$L^2（{乙}_r（X）\cap \mathrm{\Omega }）$对于每一个$X\epsilon \stackrel{￣}{\mathrm{\Omega }}$和$t$什么时候$r$足够小，这似乎具有独立的利益。另一方面，在标量值灵敏度的情况下$S=\chi （X,n,C）𝕀$，如果域是具有半径的球，则对于二维及更高维度，存在全局及时有界经典解$右$所有给定的数据都是径向的。径向情况的结果涵盖了标量值灵敏度$\chi$可以是单数的$C=0$。