Abstract
For an equation of mixed parabolic-hyperbolic type in a rectangular parallelepiped, the inverse problem of finding the factors of the right-hand side that depend on spatial variables is investigated. A criterion for the uniqueness of a solution is established. The solution is constructed as a sum of orthogonal series. When justifying the convergence of the series, the problem of small denominators of two natural arguments arose. Estimates on the separation of small denominators from zero with the corresponding asymptotics are established. These estimates made it possible to substantiate the convergence of the constructed series in the class of regular solutions of this equation.
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The reported study was funded by Russian Foundation for Basic Research, project no. 19-31-60016.
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(Submitted by E. E. Tyrtyshnikov)
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Sidorov, S.N. An Inverse Problem for an Equation of Parabolic-Hyperbolic Type to Find the Factors of the Right-Hand Side Depending on the Spatial Coordinates. Lobachevskii J Math 42, 1431–1444 (2021). https://doi.org/10.1134/S1995080221060275
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DOI: https://doi.org/10.1134/S1995080221060275