Recovery of an unknown specific heat by means of overposed data
Recovery of an unknown specific heat by means of overposed data
复制标题
通过重叠数据恢复未知的比热
DOI：
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
W. Rundell
中科院分区：
文献类型：
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作者：
M. Pilant;W. Rundell
在本文中，我们考虑一类反问题，其中未知函数 c(.) 由抛物线初始值问题确定，并且沿着边界的一部分重叠狄利克雷数据。以奇异积分方程的形式获得重叠数据和未知系数之间的映射。这是通过迭代来解决的，所得到的不动点被证明是反问题的解。给出了该方法收敛的充分条件，以及对未知热导率情况的扩展。
In this paper we consider a class of inverse problems in which an unknown function, c(.), is to be determined from a parabolic initial-value problem, with overposed Dirichlet data along a portion of the boundary. A mapping between the overposed data and the unknown coefficient is obtained in the form of a singular integral equation. This is solved by iteration, and the resulting fixed point is shown to be the solution of the inverse problem. Sufficient conditions for convergence of this method, as well as an extension to the case of an unknown thermal conductivity, are given.