论文标题
逆问题的独特性和数值重建
Uniqueness and numerical reconstruction for inverse problems dealing wit interval size search
论文作者
论文摘要
我们在一个时间间隔内考虑一个空间间隔的热方程和波动方程。本文讨论了通过管理方程解决方案的额外边界数据来确定空间间隔的大小的反问题。在几种不同的情况下，我们证明了独特性，非唯一性和一定规模的估计。此外，我们从数值上解决了反问题并计算大小的准确近似值。通过令人满意的数值实验来说明这一点。
We consider a heat equation and a wave equation in a spatial interval over a time interval. This article deals with inverse problems of determining sizes of spatial intervals by extra boundary data of solutions of the governing equations. Under several different circumstances, we prove the uniqueness, the non-uniqueness and some size estimate. Moreover, we numerically solve the inverse problems and compute accurate approximations of the sizes. This is illustrated with satisfactory numerical experiments.
