Abstract

The inverse problem about reconstruction of a function characterizing the variation of the elastic modulus in an inhomogeneous cylindrical waveguide according to information about the field of radial displacements in the far zone has been studied. A study has been carried out based on combining the Fourier transform and linearization method. Each step of the formed iteration process includes the solution of the direct problem based on the shooting method and the solution of a Fredholm integral equation of the first kind for finding the refining corrections for the sought function. The results of computational experiments are presented.

中文翻译：

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关于估计圆柱波导中径向不均匀性的定律

摘要

研究了关于根据远区域中的径向位移场的信息重建表征不均匀圆柱波导中弹性模量变化的函数的反问题。基于傅里叶变换和线性化方法的结合已经进行了研究。所形成的迭代过程的每个步骤都包括基于射击方法的直接问题的解决方案和第一类Fredholm积分方程的解决方案，用于找到所寻找函数的精细校正。给出了计算实验的结果。