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<p>This paper deals with the existence and stability of the solution for a class heat equation with logarithmic nonlinearity. Using the potential well method, we proved the existence of global solutions. Moreover, exponential stability and the rapid stabilization of solutions are obtained by energy and backstepping methods.</p>

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Existence and stability of a one-dimensional heat equation with logarithmic nonlinearity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月25日

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  • Cong Sun,
  • Yan Zhuo Jiang

摘要

This paper deals with the existence and stability of the solution for a class heat equation with logarithmic nonlinearity. Using the potential well method, we proved the existence of global solutions. Moreover, exponential stability and the rapid stabilization of solutions are obtained by energy and backstepping methods.