论文标题
用于检测分数扩散方程中可变顺序的外壳方法
The enclosure method for the detection of variable order in fractional diffusion equations
论文作者
论文摘要
本文关注的是一种新型的反向障碍物问题，该问题由有限域中的可变时间分解扩散方程控制。未知的障碍物是一个区域，其中管理方程的分数时间导数的空间因变量阶与已知的均匀背景偏离。观察数据由针对特殊设计的DIRICHLET数据的Governing方程解的Neumann数据给出。在偏差的合适跳跃条件下，可以从观察数据中提取有关障碍物的几何形状和跳跃的定性性质的最新版本，从观察数据中提取有关障碍物的几何形状的信息。
This paper is concerned with a new type of inverse obstacle problem governed by a variable-order time-fraction diffusion equation in a bounded domain. The unknown obstacle is a region where the space dependent variable-order of fractional time derivative of the governing equation deviates from a known homogeneous background one. The observation data is given by the Neumann data of the solution of the governing equation for a specially designed Dirichlet data. Under a suitable jump condition on the deviation, it is shown that the most recent version of the time domain enclosure method enables one to extract information about the geometry of the obstacle and a qualitative nature of the jump, from the observation data.
