论文标题
非线性HelmholtzSchrödinger方程和带有部分数据的时间谐波方程的逆问题
Inverse problems for nonlinear Helmholtz Schrödinger equations and time-harmonic Maxwell's equations with partial data
论文作者
论文摘要
我们认为Calderón在$ \ r^n $中的有限域中的一类非线性helmholtzschrödinger方程和麦克斯韦方程的逆边界值问题。主要方法是相应方程式的Dirichlet到Neumann地图的高阶线性化。在\ cite {dksu}之后，可获得线性化部分数据的局部唯一性。 Runge近似属性和独特的延续原理使我们能够扩展到全球情况。同时恢复了一些未知的腔$/$边界，并将系数作为某些应用程序。
We consider Calderón's inverse boundary value problems for a class of nonlinear Helmholtz Schrödinger equations and Maxwell's equations in a bounded domain in $\R^n$. The main method is the higher-order linearization of the Dirichlet-to-Neumann map of the corresponding equations. The local uniqueness of the linearized partial data Calderón's inverse problem is obtained following \cite{DKSU}. The Runge approximation properties and unique continuation principle allow us to extend to global situations. Simultaneous recovery of some unknown cavity$/$boundary and coefficients are given as some applications.
