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This paper studies the well-posedness using the semigroup approach and the asymptotic convergence of the solutions of a nonlocal phase-field model of Caginalp type as the parameter related to the nonlocal term tends to zero. We ensure that under some conditions on the initial data, the solutions of the nonlocal problem converge to the corresponding strong solution of the local problem.

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Nonlocal to Local Caginalp Model

  • 会议论文

  • 发表日期：

    2026年

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  • Juliana H. Lopes,
  • Pedro T. P. Lopes

摘要

This paper studies the well-posedness using the semigroup approach and the asymptotic convergence of the solutions of a nonlocal phase-field model of Caginalp type as the parameter related to the nonlocal term tends to zero. We ensure that under some conditions on the initial data, the solutions of the nonlocal problem converge to the corresponding strong solution of the local problem.