Scholarlink

Abstract <p>A linear integral equation related to the coefficient inverse problem for a hyperbolic equation is considered. In the inverse problem, based on measurements of scalar wave fields scattered by an inhomogeneity, it is necessary to reconstruct the propagation velocity of the signal on the inhomogeneity. Probing fields are generated by point sources centered on a circle. We prove the unique solvability of the inverse problem with such an arrangement of sources under quite general assumptions on the choice of a set of detectors. The relationship between the axial symmetry of the scattering data and the symmetry of the desired function relative to the same axis is established.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Uniqueness of the Solution to the Lavrent’ev Equation with Sources on a Circle

  • 期刊论文

  • 发表日期：

    2025年2月1日

查看全文
  • M. Yu. Kokurin

摘要

Abstract

A linear integral equation related to the coefficient inverse problem for a hyperbolic equation is considered. In the inverse problem, based on measurements of scalar wave fields scattered by an inhomogeneity, it is necessary to reconstruct the propagation velocity of the signal on the inhomogeneity. Probing fields are generated by point sources centered on a circle. We prove the unique solvability of the inverse problem with such an arrangement of sources under quite general assumptions on the choice of a set of detectors. The relationship between the axial symmetry of the scattering data and the symmetry of the desired function relative to the same axis is established.