| Abstract: |
| In two papers by C. Liu et al. (Science, 2011) and Fu et al. (Phys. Rev. Lett. 2012), a new argument driving spatio-temporal pattern formation by density suppressed motility through self-trapping was proposed and verified by a mathematical model. In this talk, we shall report some results on the density-suppressed motility model proposed therein. The main challenge arising in this model is the possible degeneracy of diffusion. In our work, we shall use the motility function as a weight function and employ the weighted energy estimates to get the boundedness of solutions and hence rule out the possible degeneracy to obtain the existence of global classical solutions. We also discuss the large-time behavior of solutions and pattern formations with numerical simulations. This is a joint work with Haiyang Jin (South China University of Technology) and Yong-Jung Kim (KAIST). |
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