| Abstrakt: |
Abstract: This paper deals with parabolic-elliptic chemotaxis systems with the sensitivity function \chi(v) and the growth term f(u) under homogeneous Neumann boundary conditions in a smooth bounded domain. Here it is assumed that 0< \chi(v)\leq{{\chi}_0}/{v^k} (k\geq1, {\chi}_0>0) and \lambda_1-\mu_1 u \leq f(u)\leq\lambda_2-\mu_2 u (\lambda_1,\lambda_2,\mu_1,\mu_2>0). It is shown that if \chi_0 is sufficiently small, then the system has a unique global-in-time classical solution that is uniformly bounded. This boundedness result is a generalization of a recent result by K. Fujie, M. Winkler, T. Yokota. |
