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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Xiaoqian Xu
Carnegie Melllon University
Title: Suppression of chemotactic explosion by mixing

Abstract: Keller-Segel equation is one of the most studied PDE models of processes involving chemical attraction. However, solution of Keller-Segel equation can exhibit dramatic collapsing behavior, where the population density of bacteria concentrates positive mass in a measure zero region. In other words, there exist initial data leading to finite time blow up. In this talk, we will discuss the possible effects resulting from interaction of chemotactic and fluid transport processes, namely we will consider the Keller-Segel equation with additional advection term modeling ambient fluid flow. We will prove that the presence of fluid can prevent the singularity formation. We will discuss two classes of flows that have the explosion arresting property. Both classes are known as very efficient mixers.

Recording: http://mm.math.cmu.edu/recordings/cna/Xiaoqian_Xu_small.mp4
Date: Tuesday, September 13, 2016
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice