MATHEMATICA BOHEMICA, Vol. 139, No. 4, pp. 639-647, 2014

Boundedness of solutions to parabolic-elliptic chemotaxis-growth systems with signal-dependent sensitivity

Kentarou Fujie, Tomomi Yokota

Kentarou Fujie, Tomomi Yokota, Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan, e-mail:,

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.

Keywords: chemotaxis; global existence; boundedness

Classification (MSC 2010): 35B40, 35K60

Full text available as PDF.

Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at

[Previous Article] [Next Article] [Contents of This Number] [Contents of Mathematica Bohemica]
[Full text of the older issues of Mathematica Bohemica at DML-CZ]