Uniqueness theorem on weak solutions to the Keller–Segel system of degenerate and singular types

Tatsuki Kawakami; Yoshie Sugiyama

doi:10.1016/j.jde.2015.11.021

Uniqueness theorem on weak solutions to the Keller–Segel system of degenerate and singular types

Tatsuki Kawakami, Yoshie Sugiyama

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

The uniqueness of weak solutions to the Keller–Segel systems of degenerate and singular types is proven in the class of Hölder continuous functions. Hölder continuity is expected to be an optimal regularity for weak solutions of the degenerate Keller–Segel systems under consideration. Our proof is based on the vanishing viscosity duality method.

Original language	English
Pages (from-to)	4683-4716
Number of pages	34
Journal	Journal of Differential Equations
Volume	260
Issue number	5
DOIs	https://doi.org/10.1016/j.jde.2015.11.021
Publication status	Published - Mar 5 2016

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jde.2015.11.021

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title = "Uniqueness theorem on weak solutions to the Keller–Segel system of degenerate and singular types",

abstract = "The uniqueness of weak solutions to the Keller–Segel systems of degenerate and singular types is proven in the class of H{\"o}lder continuous functions. H{\"o}lder continuity is expected to be an optimal regularity for weak solutions of the degenerate Keller–Segel systems under consideration. Our proof is based on the vanishing viscosity duality method.",

author = "Tatsuki Kawakami and Yoshie Sugiyama",

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AU - Sugiyama, Yoshie

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N2 - The uniqueness of weak solutions to the Keller–Segel systems of degenerate and singular types is proven in the class of Hölder continuous functions. Hölder continuity is expected to be an optimal regularity for weak solutions of the degenerate Keller–Segel systems under consideration. Our proof is based on the vanishing viscosity duality method.

AB - The uniqueness of weak solutions to the Keller–Segel systems of degenerate and singular types is proven in the class of Hölder continuous functions. Hölder continuity is expected to be an optimal regularity for weak solutions of the degenerate Keller–Segel systems under consideration. Our proof is based on the vanishing viscosity duality method.

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

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Uniqueness theorem on weak solutions to the Keller–Segel system of degenerate and singular types

Abstract

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