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In this note we consider the Keller–Segel system and the chemotaxis system with local sensing. The similarities in the mathematical structure of both systems are discussed, while the differences in the behaviour of solutions to the both systems are explained. Several open problems about the chemotaxis system with local sensing are listed and some discussion on one of them, concentration phenomena of solutions, is presented.

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A Short Note on Concentration Phenomena for Chemotaxis Systems with Local Sensing

  • 会议论文

  • 发表日期：

    2026年

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  • Kentaro Fujie

摘要

In this note we consider the Keller–Segel system and the chemotaxis system with local sensing. The similarities in the mathematical structure of both systems are discussed, while the differences in the behaviour of solutions to the both systems are explained. Several open problems about the chemotaxis system with local sensing are listed and some discussion on one of them, concentration phenomena of solutions, is presented.