A lower bound on the blow up time for solutions of a chemotaxis system with nonlinear chemotactic sensitivity

作者：Anderson Jeffrey R; Deng Keng^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2017, 159: 2-9.

DOI：10.1016/j.na.2016.11.018

• Nonlinear chemotaxis system
• Blow up time
• Global existence

In a recent study, a lower bound is established on the blow up time for solutions of a chemotaxis system, with nonlinear chemotactic sensitivity u(u + 1)(m-1), set in the three-dimensional unit ball. Here, u is the density of a cell or organism that produces a chemical, with density v, and moves preferentially toward regions of higher concentration of v according to the flux -del u-chi u(u+l)(m-l)del v. With chi > 0, v is referred to as a "chemoattractant" and, in the case m = 1, the system reduces to a version of the Keller -Segel model. Solutions that blow up in finite time have been previously established for the system on a ball in R-n provided n >= 2, m > 2/n. For technical reasons, the lower bound proven for the blow up time applies in such cases when n = 3 and m <= 2. We extend the analysis and resulting lower bound to such a model in general convex, domains, with n >= 2 and any m.

• 出版日期2017-8