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Three-Dimensional Initial-Boundary Value Problem for a Parabolic-Hyperbolic Equation with a Degenerate Parabolic Part

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Abstract

An initial-boundary value problem is studied for a nonhomogeneous equation of mixed parabolic-hyperbolic type in three variables with a degenerate parabolic part in a rectangular parallelepiped. A uniqueness criterion for its solution is established. The solution is constructed as a sum of an orthogonal series. Justifying the convergence of the series has led to the problem of small denominators of two natural arguments. Estimates on the separation of small denominators from zero with the corresponding asymptotics are established. These estimates have made it possible to substantiate the convergence of the constructed series in the class of regular solutions of this equation. The stability of the solution with respect to the boundary function and the right-hand side of the equation is established.

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Funding

This work is supported by the Russian Foundation for Basic Research (project no. 19-31-60016).

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Authors and Affiliations

  1. Ufa State Petroleum Technological University, 450064, Ufa, Russia

    S. N. Sidorov

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  1. S. N. Sidorov
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Correspondence to S. N. Sidorov.

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Translated by M. Talacheva

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Sidorov, S.N. Three-Dimensional Initial-Boundary Value Problem for a Parabolic-Hyperbolic Equation with a Degenerate Parabolic Part. Russ Math. 67, 44–55 (2023). https://doi.org/10.3103/S1066369X23040047

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