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A note on Monge–Amp`ere Keller–Segel equation

Hui Huang Tsinghua University Jian-Guo Liu Duke University

Analysis of PDEs mathscidoc:1702.03024

Applied Mathematics Letters, 11, 26–34, 2016.11
This note studies the Monge-Ampère Keller–Segel equation in a periodic domain , a fully nonlinear modification of the Keller–Segel equation where the Monge-Ampère equation substitutes for the usual Poisson equation . The existence of global weak solutions is obtained for this modified equation. Moreover, we prove the regularity in for some .
Chemotaxis; Polar factorization; Convex potential; Brenier map; Global existence
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@inproceedings{hui2016a,
  title={A note on Monge–Amp`ere Keller–Segel equation},
  author={Hui Huang, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207222353566418269},
  booktitle={Applied Mathematics Letters},
  volume={11},
  pages={26–34},
  year={2016},
}
Hui Huang, and Jian-Guo Liu. A note on Monge–Amp`ere Keller–Segel equation. 2016. Vol. 11. In Applied Mathematics Letters. pp.26–34. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207222353566418269.
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