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<p>Under consideration are inverse problems of recovering the right-hand side (the source function) in a&#xa0;parabolic system from mixed overdetermination data, i.e., some integral data and the values of a&#xa0;solution at some collections of interior points are given. A solution to the parabolic system is generalized and distributions of certain classes can occur into the right-hand side. Under certain conditions, it is proven that this inverse problem is well-posed in Sobolev classes. A numerical algorithm is developed and the results of numerical experiments are exhibited.</p>

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Inverse problems of recovering mixed sources in convection-diffusion systems

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Sergey G. Pyatkov,
  • Sergey A. Shmorgan

摘要

Under consideration are inverse problems of recovering the right-hand side (the source function) in a parabolic system from mixed overdetermination data, i.e., some integral data and the values of a solution at some collections of interior points are given. A solution to the parabolic system is generalized and distributions of certain classes can occur into the right-hand side. Under certain conditions, it is proven that this inverse problem is well-posed in Sobolev classes. A numerical algorithm is developed and the results of numerical experiments are exhibited.