<p>This paper focuses on determining the source term in coupled nonlocal diffusion equations from interior domain observations. Through Laplace transform argument, we establish a weak unique continuation principle for the solution of the system. By combining this principle with the Duhamel principle, we establish the uniqueness of the inverse source problem. For numerical simulations, we introduce an iterative threshold algorithm. Various numerical experiments are presented to validate the accuracy and efficiency of the algorithm.</p>

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Uniqueness for an inverse source problem for weakly coupling nonlocal diffusion equations from interior measurement

  • Beibei Fan,
  • Zhiyuan Li

摘要

This paper focuses on determining the source term in coupled nonlocal diffusion equations from interior domain observations. Through Laplace transform argument, we establish a weak unique continuation principle for the solution of the system. By combining this principle with the Duhamel principle, we establish the uniqueness of the inverse source problem. For numerical simulations, we introduce an iterative threshold algorithm. Various numerical experiments are presented to validate the accuracy and efficiency of the algorithm.