Lipschitz stability in the determination of the principal part of a parabolic equation
Lipschitz stability in the determination of the principal part of a parabolic equation
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DOI：
10.1051/cocv:2008043
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发表时间：
2009-07
期刊：
影响因子：
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通讯作者：
Ganghua Yuan;Ganghua Yuan;Masahiro Yamamoto
中科院分区：
文献类型：
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作者：
Ganghua Yuan;Ganghua Yuan;Masahiro Yamamoto
设y（h）（t，x）是具有非齐次项h，和的一个解，其中是一个有界区域.本文讨论了在适当地选择输入源后，确定n（n+1）/2个未知函数aij的反问题，其中是任意子边界，表示法向导数，和.在的情况下，我们证明了Lipschitz稳定性的反问题，如果我们选择从一个集合与一个任意固定的子域。此外，我们还可以通过特殊的选择，。这个证明是基于Carleman的估计。
Let y(h)(t,x) be one solution to with a non-homogeneous term h , and , where is a bounded domain. We discuss an inverse problem of determining n(n+1)/2 unknown functions a ij by , after selecting input sources suitably, where is an arbitrary subboundary, denotes the normal derivative, and . In the case of , we prove the Lipschitz stability in the inverse problem if we choose from a set with an arbitrarily fixed subdomain . Moreover we can take by making special choices for , . The proof is based on a Carleman estimate.