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<p>This article is devoted to the detection of parameters in anomalous diffusion from a single passive measurement. More precisely, we consider the simultaneous identification of coefficients as well as a time-dependent source term appearing in a time-fractional diffusion equation from a single boundary or internal passive measurement. We obtain several uniqueness results in dimension one as well as a multidimensional extension under some symmetry assumptions. Our analysis relies on spectral representation of solutions, complex and harmonic analysis combined with some known inverse spectral results for Sturm–Liouville operators. The theoretical results are complemented by a corresponding reconstruction algorithm and numerical simulations.</p>

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Simultaneous identification of coefficients and source in a subdiffusion equation from one passive measurement

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • Maolin Deng,
  • Ali Feizmohammadi,
  • Bangti Jin,
  • Yavar Kian

摘要

This article is devoted to the detection of parameters in anomalous diffusion from a single passive measurement. More precisely, we consider the simultaneous identification of coefficients as well as a time-dependent source term appearing in a time-fractional diffusion equation from a single boundary or internal passive measurement. We obtain several uniqueness results in dimension one as well as a multidimensional extension under some symmetry assumptions. Our analysis relies on spectral representation of solutions, complex and harmonic analysis combined with some known inverse spectral results for Sturm–Liouville operators. The theoretical results are complemented by a corresponding reconstruction algorithm and numerical simulations.