论文标题
平面波的双曲线方程的3D系数反问题的Hölder稳定性估计值
A Hölder Stability Estimate for a 3D Coefficient Inverse Problem for a Hyperbolic Equation With a Plane Wave
论文作者
论文摘要
考虑了具有未确定数据的双曲线方程的3D系数反问题。正向问题是与初始条件的库奇问题，增量功能集中在单个平面（即平面波）上。与三个空间变量中的两个，即“部分有限的差异”，某个相关的操作员以有限差异而编写。网格步长的大小从下面的固定数字界定。使用卡尔曼估计值首次获得此问题的Hölder稳定性估计。另一个新的结果是，从特征性楔形物附近的前向问题解决方案扩展的第一项幅度的幅度估算了一个估计。
A 3D coefficient inverse problem for a hyperbolic equation with non-overdetermined data is considered. The forward problem is the Cauchy problems with the initial condition the delta function concentrated at a single plane (i.e. the plane wave). A certain associated operator is written in finite differences with respect to two out of three spatial variables, i.e. "partial finite differences". The grid step size is bounded from the below by a fixed number. A Carleman estimate is applied to obtain, for the first time, a Hölder stability estimates for this problem. Another new result is an estimate from the below of the amplitude of the first term of the expansion of the solution of the forward problem near the characteristic wedge.
