The Fractional Diffusion Limit of a Kinetic Model with Biochemicak Pathway
发布时间：2017年10月09日
浏览次数：6655
发布者: Xiaoni Tan
主讲人： Min Tang (Shanghai Jiao Tong University)
活动时间： 从 2017-10-11 10:00 到 11:00
场地： 北京国际数学研究中心，镜春园82号甲乙丙82J04教室
Kinetic-transport equations that take into account the intra-cellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their relations to more standard models. Macroscopic equations of Keller-Segel type have been derived using parabolic scaling. Due to the randomness of receptor methylation or intra-cellular chemical reactions, noise occurs in the signaling pathways and aspects the tumbling rate. Then, comes the question to understand the role of an internal noise on the behavior of the full population. In this talk we consider a kinetic model for chemotaxis which includes biochemical pathway with noises. We show that under proper scaling and conditions on the tumbling frequency as well as the form of noise, fractional diffusion can arise in the macroscopic limits of the kinetic equation. This gives a new mathematical theory about how long jumps can be due to the internal noise of the bacteria.
