论文标题
同时从Cauchy数据中恢复潜力和点源
Recovering simultaneously a potential and a point source from Cauchy data
论文作者
论文摘要
本文致力于从相关的非线性dirichlet到neumann映射的shrödinger方程中同时恢复电位和点源的反问题。证明了反转的独特性，并得出了对数稳定性估计。众所周知，仅在了解源时仅确定电势的反问题是不适合的。相比之下，当给出电势时识别点源的问题是很好的。获得的结果表明，Neumann Map的非线性Dirichlet包含足够的信息以同时确定势和点源。然而，恢复嵌入未知背景介质的点源变成了不良反转。
This paper is devoted to the inverse problem of recovering simultaneously a potential and a point source in a Shrödinger equation from the associated nonlinear Dirichlet to Neumann map. The uniqueness of the inversion is proved and logarithmic stability estimates are derived. It is well known that the inverse problem of determining only the potential while knowing the source, is ill-posed. In contrast the problem of identifying a point source when the potential is given is well posed. The obtained results show that the nonlinear Dirichlet to Neumann map contains enough information to determine simultaneously the potential and the point source. However recovering a point source imbedded in an unknown background medium becomes an ill-posed inversion.
