Determining the temperature from incomplete boundary data
Determining the temperature from incomplete boundary data
复制标题
从不完整的边界数据确定温度
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
B. Johansson
中科院分区：
文献类型：
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作者：
B. Johansson
给出了一种由部分边界上的柯西数据确定温度场的迭代方法。在每一步迭代中，求解热算子及其伴随算子的一系列混合适定边值问题。给出了该方法在加权L2空间中的收敛证明，以及在有噪声数据情况下的停止准则。此外，还给出了二阶抛物型混合边界条件初边值问题在加权Sobolev空间中的可解性结果。证明了解的正则性。(2007 Wiley-VCH Verlag GmbH&Co.KGaA，Weinheim)
An iterative procedure for determining temperature fields from Cauchy data given on a part of the boundary is presented. At each iteration step, a series of mixed well‐posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L2‐space is included, as well as a stopping criteria for the case of noisy data. Moreover, a solvability result in a weighted Sobolev space for a parabolic initial boundary value problem of second order with mixed boundary conditions is presented. Regularity of the solution is proved. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)