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Determining the Coefficient of a Mixed Parabolic-Hyperbolic Equation with Noncharacteristic Type Change Line

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Abstract

Direct and inverse problems for a model equation of the mixed parabolic-hyperbolic type are studied. The direct problem is an analog of the Tricomi problem for this equation with noncharacteristic type change line. The unknown in the inverse problem is the variable coefficient multiplying a lower-order term in the hyperbolic equation. To determine it, we study the inverse problem in which the overdetermination condition on the characteristics is set for the solution defined in the hyperbolic part of the domain of the direct problem; namely, the value of the normal derivative on one characteristic and the value of the function itself on the other characteristic is prescribed. Theorems on the unique solvability of the problems in the sense of the classical solution are proved.

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Authors and Affiliations

  1. Bukhara Branch of Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, Bukhara, Uzbekistan

    D. K. Durdiev

  2. Bukhara State University, Bukhara, 705018, Uzbekistan

    D. K. Durdiev

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  1. D. K. Durdiev
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Correspondence to D. K. Durdiev.

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Translated by V. Potapchouck

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Durdiev, D.K. Determining the Coefficient of a Mixed Parabolic-Hyperbolic Equation with Noncharacteristic Type Change Line. Diff Equat 58, 1618–1629 (2022). https://doi.org/10.1134/S00122661220120059

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  • DOI: https://doi.org/10.1134/S00122661220120059

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