Geodesic
The Duhamel method in the inverse problems for hyperbolic equations. II
Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 4, pp. 3-18

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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.
Keywords: inverse problem, wave equation, integral condition. 
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     author = {A. N. Artyushin},
     title = {The {Duhamel} method in the inverse problems for hyperbolic equations. {II}},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2019_22_4_a0/}
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A. N. Artyushin. The Duhamel method in the inverse problems for hyperbolic equations. II. Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 4, pp. 3-18. http://geodesic.mathdoc.fr/item/SJIM_2019_22_4_a0/