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The Duhamel Method in the Inverse Problems for Hyperbolic Equations. II
Journal of Applied and Industrial Mathematics Pub Date : 2020-02-04 , DOI: 10.1134/s199047891904001x
A. N. Artyushin

Under consideration is the identification problem for a time-dependent source in the wave equation. The Dirichlet conditions are used as the boundary conditions, whereas the weighted integral of the conormal derivative of the solution over the boundary of the spatial domain serves as the overdetermination condition. Using the Duhamel method, the problem is reduced to the Volterra integral equation of the first and then the second kind. These results are applied to studying nonlinear coefficient problems. The existence and uniqueness of a local solution is proved by the contraction mapping principle.

中文翻译:

双曲方程反问题中的Duhamel方法。II

正在考虑的是波动方程中与时间有关的源的识别问题。Dirichlet条件用作边界条件,而在空间域边界上的解的标准正态导数的加权积分用作超确定条件。使用Duhamel方法,将问题简化为第一类和第二类的Volterra积分方程。这些结果被用于研究非线性系数问题。压缩映射原理证明了局部解的存在性和唯一性。
更新日期:2020-02-04
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