| Abstract: |
| To understand the ``self-trapping'' mechanism inducing spatio-temporal pattern formations observed in the experiment of for bacterial motion, the density-suppressed motility model was proposed. The purpose of this paper is to consider the Cauchy problem with the motility function $\gamma(v)=\frac{1}{(1+v)^m}$, we obtain that the condition $0\le m\le \frac{2}{(N-2)_+}$ can warrant the global boundedness of solutions, based on which the asymptotic spreading behavior for solutions which are observed for genuine patterns in the experiment is verified. |
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