An Inverse Problem for Maxwell's Equations in Anisotropic Media*
An Inverse Problem for Maxwell's Equations in Anisotropic Media*
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DOI：
10.1007/s11401-005-0572-3
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发表时间：
2007
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影响因子：
--
通讯作者：
Shumin Li;Masahiro Yamamoto
中科院分区：
文献类型：
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作者：
Shumin Li;Masahiro Yamamoto
摘要作者考虑了二维等磁各向异性非均匀介质的麦克斯韦方程，并讨论了由有限数量的横向边界测量确定本构关系中的介电常数张量$$\Left({\Begin{μ}{*{20}c}{{\varepsilon_{1}})和{{\varepsilon_{2}{\varepsilon_{2}&{{\varepsilon_{3}\\End{Arrow}}\Right)}$$的反问题。当ε1，ε2，ε3，μ满足一定的先验条件时，应用Carleman估计，证明了Lipschitz型稳定性估计.
AbstractThe authors consider Maxwell's equations for an isomagnetic anisotropic and inhomogeneous medium in two dimensions, and discuss an inverse problem of determining the permittivity tensor $$ {\left( {\begin{array}{*{20}c} {{\varepsilon _{1} }} & {{\varepsilon _{2} }} \\ {{\varepsilon _{2} }} & {{\varepsilon _{3} }} \\ \end{array} } \right)} $$ and the permeabilityμin the constitutive relations from a finite number of lateral boundary measurements. Applying a Carleman estimate, the authors prove an estimate of the Lipschitz type for stability, provided that ε1, ε2, ε3,μsatisfy some a priori conditions.