Geodesic
Inverse problems for a two-dimensional heat equation with unknown right-hand side
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2021), pp. 83-97

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Based on the solution of the first initial-boundary value problem for the inhomo-geneous two-dimensional heat equation, the inverse problems are posed and studied to find the factors of the right-hand side depending on spatial variables and time. Previously, the solution of the direct initial-boundary-value problem is constructed explicitly. The uniqueness of the solution of the direct and inverse problems is proved on the basis of the completeness property of the system of eigenfunctions of the corresponding homogeneous Dirichlet problem for the Laplace operator. Existence theorems for solving inverse problems are established. The solutions of which are built explicitly.
Keywords: heat equation, initial-boundary value problem, inverse problem, uniqueness, series, integral equation.
Mots-clés : existence 
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     author = {K. B. Sabitov and A. R. Zainullov},
     title = {Inverse problems for a two-dimensional heat equation with unknown right-hand side},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {83--97},
     publisher = {mathdoc},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_3_a7/}
}
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K. B. Sabitov; A. R. Zainullov. Inverse problems for a two-dimensional heat equation with unknown right-hand side. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2021), pp. 83-97. http://geodesic.mathdoc.fr/item/IVM_2021_3_a7/