We consider a class of logarithmic Keller-Segel type systems modeling the spatio-temporal behavior of either chemotactic cells or criminal activities in spatial dimensions two and higher. Under certain assumptions on parameter values and given functions, the existence of classical solutions is established globally in time, provided that initial data are sufficiently regular. In particular, we enlarge the range of chemotactic sensitivity χ, compared to known results, in case that spatial dimensions are between two and eight. In addition, we provide new type of small initial data to obtain global classical solution, which is also applicable to the urban crime model. We discuss long-time asymptotic behaviors of solutions as well.

我们考虑一类对数Keller-Segel类型的系统，该系统对空间尺寸为2或更高的趋化细胞或犯罪活动的时空行为进行建模。在参数值和给定函数的某些假设下，只要初始数据足够规则，经典解决方案的存在就会在全球范围内及时建立。特别是，如果空间尺寸在2到8之间，则与已知结果相比，我们扩大了趋化敏感性χ的范围。另外，我们提供了新的小型初始数据类型以获得全局经典解，这也适用于城市犯罪模型。我们还讨论了解决方案的长期渐近行为。