Stability estimate for an inverse problem for the wave equation in a magnetic field
Stability estimate for an inverse problem for the wave equation in a magnetic field
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磁场中波动方程反问题的稳定性估计
DOI：
10.1080/00036810801911264
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发表时间：
2008
影响因子：
1.1
通讯作者：
Hajer Benjoud
中科院分区：
文献类型：
--
作者：
M. Bellassoued;Hajer Benjoud
在这篇文章中，我们证明了由边界观测值确定进入磁波动方程的磁场的反问题的稳定性估计。这些信息包含在与磁波方程解相关的双曲（动态）狄利克雷-诺依曼映射中。在d ≥ 2维中，我们证明了在边界上测得的磁波动方程的Dirichlet-to-Neumann映射的知识唯一地决定了磁场，并且我们证明了在决定由磁势引起的磁场时的Hölder型稳定性.
In this article, we prove stability estimate of the inverse problem of determining the magnetic field entering the magnetic wave equation in a bounded smooth domain in ℝ d from boundary observations. This information is enclosed in the hyperbolic (dynamic) Dirichlet-to-Neumann map associated to the solutions to the magnetic wave equation. We prove in dimension d ≥ 2 that the knowledge of the Dirichlet-to-Neumann map for the magnetic wave equation measured on the boundary determines uniquely the magnetic field and we prove a Hölder-type stability in determining the magnetic field induced by the magnetic potential.
DOI：
10.1201/9781420036220
发表时间：
2001-07
期刊：
--
影响因子：
--
作者：
A. Katchalov;Y. Kurylev;M. Lassas
通讯作者：
A. Katchalov;Y. Kurylev;M. Lassas