  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 chemotatic sensitivity $\chi$, 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.
