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Tricomi Problem for Mixed Parabolic–Hyperbolic Equation with Higher Order Boundary Condition

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Abstract

In this paper, we study an analogue of Tricomi problem for a parabolic–hyperbolic equation. One boundary condition in the parabolic part of the domain contains the third derivative of the space variable. A spectral problem with a spectral parameter in the boundary condition arises, when solving this problem. The system of eigenfunctions of this problem (after removing any one eigenfunction) forms a Riesz basis. The conditions for the correctness of the formulated Tricomi problem are found.

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Funding

The research is financially supported by a grant from the Ministry of Science and Education of the Republic of Kazakhstan (No. AP13067805).

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Author notes

  1. Bauyrzhan Derbissaly and Makhmud Sadybekov contributed equally to this work.

Authors and Affiliations

  1. Department of Differential Equations, Institute of Mathematics and Mathematical Modeling, Pushkin, 050010, Almaty, Kazakhstan

    Bauyrzhan Derbissaly & Makhmud Sadybekov

  2. Department of Mathematics, Al-Farabi Kazakh National University, al-Farabi, 050040, Almaty, Kazakhstan

    Bauyrzhan Derbissaly

Authors
  1. Bauyrzhan Derbissaly
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  2. Makhmud Sadybekov
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Contributions

This work was carried out in collaboration between both authors. MS designed the study and guided the research. BD performed the analysis and wrote the first draft of the manuscript. MS and BD managed the analysis of the study. Both authors read and approved the final manuscript.

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Correspondence to Bauyrzhan Derbissaly.

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Communicated by Sohrab Shahshahani.

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Derbissaly, B., Sadybekov, M. Tricomi Problem for Mixed Parabolic–Hyperbolic Equation with Higher Order Boundary Condition. Bull. Iran. Math. Soc. 49, 52 (2023). https://doi.org/10.1007/s41980-023-00793-5

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  • DOI: https://doi.org/10.1007/s41980-023-00793-5

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