本项目主要研究三个重要生物过程的新模型或新问题。由森林中山松甲虫的聚集行为所驱动，我们研究具间接信号产出的chemotaxis模型解的无限时间爆破的新临界质量现象。其次，定性分析描述“珊瑚四散产卵现象”中趋化性与流体相互作用的Keller-Segel-Stokes模型古典解的整体存在性、有界性和大时间行为。我们还探索刻画癌细胞浸润其周围正常组织过程的耦合的chemotaxis-haptotaxis模型有界解的渐近性态。以上三个新问题目前缺少有效的研究方法,这成为本课题的难点所在。本项目旨在这几个问题的理论研究上取得新进展或突破。

This project focuses on the study of three new models or new problems arising from significant biological processes. Motivated by the aggregative behavior of the Mountain Pine Beetle in forest habitat, we investigate a novel type of critical mass phenomenon for infinite-time blow-up in a chemotaxis model with indirect signal production. We next qualitatively deal with the global existence, boundedness and large time behavior of solutions to the Keller-Segel-Stokes model, which describes the interaction between chemotaxis and a flowing fluid in the circumstance of broadcast coral spawning. We also explore the asymptotic behavior of bounded solutions to a coupled chemotaxis-haptotaxis model addressing the process of cancer invasion of neighboring healthy tissue. An essential challenge of this proposal lies in the lack of available approaches for the aforementioned three new problems. This program aims at achieving some new progress or breakthrough in the theoretical study of the aforesaid problems.