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SUMMARY:Yao Yao (Georgia Institute of Technology)
DTSTART:20200730T140000Z
DTEND:20200730T145000Z
DTSTAMP:20260423T035604Z
UID:IMS/47
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IMS/47/">Agg
 regation-diffusion equation: symmetry\, uniqueness and non-uniqueness of s
 teady states</a>\nby Yao Yao (Georgia Institute of Technology) as part of 
 PDE seminar via Zoom\n\n\nAbstract\nThe aggregation-diffusion equation is 
 a nonlocal PDE driven by two competing effects: local repulsion modeled by
  nonlinear diffusion\, and long-range attraction modeled by nonlocal inter
 action. I will talk about how this equation arises in modeling the collect
 ive motion of cells\, and discuss several qualitative properties of its st
 eady states and dynamical solutions. Using continuous Steiner symmetrizati
 on techniques\, we show that all steady states are radially symmetric up t
 o a translation. (joint work with Carrillo\, Hittmeir and Volzone). In a r
 ecent work\, we further investigate whether they are unique within the rad
 ial class\, and show that for a given mass\, uniqueness/non-uniqueness of 
 steady states are determined by the power of the degenerate diffusion\, wi
 th the critical power being m = 2. (joint work with Delgadino and Yan.)\n
LOCATION:https://researchseminars.org/talk/IMS/47/
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