论文标题
对于schrödinger方程的逆源问题，解决方案的清晰唯一性和稳定性
Sharp uniqueness and stability of solution for an inverse source problem for the Schrödinger equation
论文作者
论文摘要
手稿与$ r（t）f（x）$在schrödinger方程的右侧$ r（t）f（x）$确定的源$ f（x）$确定源任期的空间变化因子$ f（x）$的唯一性和稳定性有关。为了建立这些结果，我们提供了一个简单的证明，证明了cauchy问题的对数条件稳定性，用于schrödinger方程，并具有时间无关系数，以及整个边界上的零dirichlet边界条件，以及对解决方程的cauchy问题的独特性证明，该方程与schrödinger方程有关，该方程与较小部分边界的独特数据有关。我们不假定子公司上的任何几何约束，时间间隔是任意的。关键是一个积分变换，一个内核解决了1-DSchrödinger的无效可控性问题，该问题将Schrödinger方程的解变为椭圆方程的解。
The manuscript is concerned with uniqueness and stability for inverse source problem of determining spatially varying factor $f(x)$ of a source term given by $R(t)f(x)$ with suitable given $R(t)$ in the right hand side of the Schrödinger equation with time independent coefficients. In order to establish these results we provide a simple proof of a logarithmic conditional stability of the Cauchy problem for the Schrödinger equation with time-independent coefficients and the zero Dirichlet boundary conditions on the whole boundary and a proof of uniqueness of solution to the Cauchy problem for the Schrödinger equation with data on an arbitrary small part of a lateral boundary. We do not assume any geometrical constraints on subboundary and a time interval is arbitrary. The key is an integral transform, with a kernel solving a null controllability problem for the 1-D Schrödinger, which changes a solution of the Schrödinger equation to a solution of an elliptic equation.
