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The First Boundary Problem for a Mixed Type Equation with Characteristic Degeneracy with Discontinuous Frankl Condition

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Abstract

For an equation of mixed elliptic-hyperbolic type of the second kind, the boundary problem in a rectangular region is studied. The criterion of uniqueness is established. The solution is built as a sum row. When substantiating convergence, the problem of small denominators. In this connection, estimates of separation from zero small denominators with the corresponding asymptotics, which and allowed us to justify the existence of a solution in the class of regular solutions and solution stability from boundary data.

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Funding

This work was partially supported by the Russian Foundation for Basic Research, project no. 18-31-00111.

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Authors and Affiliations

  1. Sterlitamak Branch of Bashkir State University, 453100, Sterlitamak, Russia

    Yu. Sabitova

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  1. Yu. Sabitova
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Correspondence to Yu. Sabitova.

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(Submitted by F. G. Avkhadiev)

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Sabitova, Y. The First Boundary Problem for a Mixed Type Equation with Characteristic Degeneracy with Discontinuous Frankl Condition. Lobachevskii J Math 41, 2269–2281 (2020). https://doi.org/10.1134/S1995080220110207

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  • DOI: https://doi.org/10.1134/S1995080220110207

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