一类基于Robin边界条件变化的反传输特征值问题

A class of inverse transmission eigenvalue problems based on the variation of the Robin boundary conditions

本文研究具有Robin边界条件的Schrodinger算子反传输特征值问题,旨在由传输特征值数据还原势函数.通过改变其中一个边界条件参数,可以获得有无穷多个能量有限的传输特征值.本文证明这样的传输特征值集合可以唯一地确定Schrodinger算子的势函数及另一个边界条件参数.

In this paper,we study the inverse transmission eigenvalue problem for the Schrodinger operator with the Robin boundary conditions,which consists in recovering the potential function from the transmission eigenvalues.By changing the value of the parameter in one of the Robin boundary conditions,we obtain infinitely many transmission eigenvalues,whose corresponding energies are finite.We prove that the set of these transmission eigenvalues uniquely determines the potential of the Schrodinger operator and one parameter in the other boundary condition.