学术报告
报告题目：Ona class of Keller-Segel chemotaxis systems with cross-diffusion
报告人：向田博士（中国人民大学）
报告时间：2015年9月3日下午3:00--4:00
报告地点：4号楼4318室
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数学学院
2015年8月27日
报告摘要：
Westudy a class of Keller–Segelchemotaxis systems with cross-diffusion. By using the entropydissipation method and assuming mainly the chemotactic sensitivityseparates the cell density and the chemical signal, we firstestablish the existence of global weak solutions with the effects ofcross diffusion included in ≤3-D.Then we show there is a critical cross diffusion rate δcsuch that no patterns may be expected for δ≥δc,while patterns are formed for δ<δcand their stability is also derived. In particular, in 1-D, patternsare always formed whenever δ<δcand the chemotactic coefficient is larger than an expressiblebifurcation value, and there is another critical cross diffusion rateδc<δcsuchthat cells with cross-diffusion rate δ∈(δc,δc)are stable, while, for cells with δ<δc to be stable, theirdegradation rate must be less than a threshold value. Hence, in somesense, cross-diffusion is harmful to enable pattern formation, whileit is helpful to stabilize the cells once patterns are formed.Finally, we show that the cross diffusion plays a role inregularizing the cell aggregation phenomenon for large chemotacticcoefficient. Our results provide global dynamics and insights on howthe biological parameters, especially, the cross diffusion, affectpattern formations。