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<p>In this paper, deals with the analysis of the internal control of a nonlocal-in-time semilinear heat equation. In our main result, we prove the exact controllability to the trajectories with distributed controls, locally supported in space. The main ingredients of the proof are an appropriate observability inequality of Carleman, a compactness-uniqueness argument, and Kakutani’s Fixed-Point Theorem in a suitable functional setting. Also, the null controllability with fewer hypotheses of term nonlinear, other possible extensions, and open problems on the nonlocal-in-time semilinear equation are presented.</p>

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Exact Controllability to the Trajectories for a Nonlocal-in-time Semilinear Heat Equation

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • Dany Nina Huaman

摘要

In this paper, deals with the analysis of the internal control of a nonlocal-in-time semilinear heat equation. In our main result, we prove the exact controllability to the trajectories with distributed controls, locally supported in space. The main ingredients of the proof are an appropriate observability inequality of Carleman, a compactness-uniqueness argument, and Kakutani’s Fixed-Point Theorem in a suitable functional setting. Also, the null controllability with fewer hypotheses of term nonlinear, other possible extensions, and open problems on the nonlocal-in-time semilinear equation are presented.