基于电磁波反问题的一类非线性积分方程解的唯一性

Uniqueness of Solutions for a Class of Nonlinear Integral Equations based on Electromagnetic Inverse Problems

液晶电磁波反问题研究对于液晶在偏振成像技术领域的应用有重要作用,所反演的材料参数为液晶经典理论的推进提供了重要的参考价值。反问题的求解过程中证明解的唯一性是克服反问题不适定性的难点之一。由于材料结构复杂且所能测量的偏振数据较为有限,液晶电磁波反问题往往具有极度不适定性。因此,文章讨论了向列型液晶电磁波反问题求解过程中的一类典型非线性积分方程,并采用经典方法证明了方程解在满足严格单调且一阶导函数连续时的唯一性。

The research on the electromagnetic inverse problem of liquid crystal plays an important role in the field of polarimetry imaging of liquid crystal.In addition,the reconstruction of material parameters provides im⁃portant reference for the advancement of the classical liquid crystal theory.Proving the uniqueness of the solu⁃tion is one of the difficulties to overcome the ill-posednessof the inverse problem.Due to the complex structure of materials and the limited data that can be measured,the inverse electromagnetic wave problem of liquid crys⁃tal is often extremely ill-posed.This paper discussed a class of typical nonlinear integral equations for solving⁃electromagnetic inverse problems of nematic liquid crystals,and by using classical methods,we prove the uniqueness of the solution when itisa strict monotone and smooth function.