Logarithmic stability in determination of a 3D viscoelastic coefficient and a numerical example
Logarithmic stability in determination of a 3D viscoelastic coefficient and a numerical example
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DOI：
10.1088/0266-5611/26/9/095006
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发表时间：
2010-09
期刊：
影响因子：
2.1
通讯作者：
Maya de Buhan;A. Osses
中科院分区：
文献类型：
--
作者：
Maya de Buhan;A. Osses
证明了三维粘弹性反问题的Carleman估计和对数稳定性估计。更确切地说，我们获得对数稳定性的反问题恢复的粘弹性系数的形式p（x）h（t）的空间部分从一个独特的测量上的任意部分的边界。主要假设h′（0）= 0，，p在边界邻域内已知，参考轨迹的正则性和灵敏性.我们提出了一种数值求解的方法，并通过一个数值例子来说明理论结果。
We prove a Carleman estimate and a logarithmic stability estimate for an inverse problem in three-dimensional viscoelasticity. More precisely, we obtain logarithmic stability for the inverse problem of recovering the spatial part of a viscoelastic coefficient of the form p(x)h(t) from a unique measurement on an arbitrary part of the boundary. The main assumptions are h′(0) = 0, , p is known in a neighborhood of the boundary and regularity and sensitivity of the reference trajectory. We propose a method to solve the problem numerically and illustrate the theoretical result by a numerical example.