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<p>This paper studies the parabolic Keller-Segel system, a mathematical model describing chemotaxis phenomena in bounded domains with smooth boundaries. Using the framework of Morrey spaces, we establish the existence, uniqueness, and exponential stability of asymptotically almost periodic mild solutions. Advanced functional analysis techniques, including dispersive estimates for the Neumann heat semigroup and Duhamel’s principle, are employed. These results contribute to the theoretical understanding of chemotactic behavior and its applications in biological systems.</p>

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Existence and Stability of Asymptotically Almost Periodic Solutions for the parabolic Keller-Segel System

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • Hassan Khaider,
  • Mohamed El Ouaarabi,
  • Abderrahmane Raji

摘要

This paper studies the parabolic Keller-Segel system, a mathematical model describing chemotaxis phenomena in bounded domains with smooth boundaries. Using the framework of Morrey spaces, we establish the existence, uniqueness, and exponential stability of asymptotically almost periodic mild solutions. Advanced functional analysis techniques, including dispersive estimates for the Neumann heat semigroup and Duhamel’s principle, are employed. These results contribute to the theoretical understanding of chemotactic behavior and its applications in biological systems.