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<p>This paper studies the controllability for a Keller–Segel type chemotaxis model with singular sensitivity. Based on the Hopf–Cole transformation, a nonlinear parabolic system, which has first-order couplings, and the coupling coefficients are functions that depend on both time and space variables, is derived. Then, the controllability result is proved by a new global Carleman estimate for general coupled parabolic equations allowed to contain a convective term. Also, the global existence of nonnegative solution for the chemotaxis system is discussed.</p>

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Exact Controllability to Nonnegative Trajectory for a Chemotaxis System

  • 期刊论文

  • 发表日期：

    2025年1月22日

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  • Qiang Tao,
  • Muming Zhang

摘要

This paper studies the controllability for a Keller–Segel type chemotaxis model with singular sensitivity. Based on the Hopf–Cole transformation, a nonlinear parabolic system, which has first-order couplings, and the coupling coefficients are functions that depend on both time and space variables, is derived. Then, the controllability result is proved by a new global Carleman estimate for general coupled parabolic equations allowed to contain a convective term. Also, the global existence of nonnegative solution for the chemotaxis system is discussed.