A note on $L^{\infty}$-bound and uniqueness to a degenerate Keller-Segel model

Jian-Guo Liu Duke University Jinhuan Wang Liaoning University

Analysis of PDEs mathscidoc:1702.03027

Acta Applicandae Mathematicae, 142, (1), 173–188, 2016.4
Abstract In this note we establish the uniform (Formula presented.)-bound for the weak solutions to a degenerate Keller-Segel equation with the diffusion exponent (Formula presented.) under a sharp condition on the initial data for the global existence. As a consequence, the uniqueness of the weak solutions is also proved.
Displacement convexity · Log-Lipschitz · Yudovich’s type theorem · Stability in Wasserstein metric
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  title={A note on $L^{\infty}$-bound and uniqueness to a degenerate Keller-Segel model},
  author={Jian-Guo Liu, and Jinhuan Wang},
  booktitle={Acta Applicandae Mathematicae},
Jian-Guo Liu, and Jinhuan Wang. A note on $L^{\infty}$-bound and uniqueness to a degenerate Keller-Segel model. 2016. Vol. 142. In Acta Applicandae Mathematicae. pp.173–188. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207225538231856272.
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