THE BITSADZE–SAMARSKY TYPE PROBLEM FOR A MIXED-TYPE EQUATION WITH SINGULAR COEFFICIENTS

THE BITSADZE–SAMARSKY TYPE PROBLEM FOR A MIXED-TYPE EQUATION WITH SINGULAR COEFFICIENTS

Authors

  • Kholtojibaevich Institute of Mathematics Academy of Sciences of the Republic of Uzbekistan
  • Taxirjonovna Institute of Mathematics Academy of Sciences of the Republic of Uzbekistan

DOI:

https://doi.org/10.52754/16948645_2023_2_115

Keywords:

boundary value problem, singular coefficient, singular integral equation with Cauchy kernel, mixed type equation, index of equation

Abstract

For an equation of mixed elliptic-hyperbolic type with singular coefficients in an unbounded domain, a nonlocal problem with generalized fractional differentiation operators whose kernels generalized Gaussian hypergeometric functions is studied. Applying the method of integral equations, the consideration problem is equivalently reduced to solving a singular integral equation with the Cauchy kernel. Regularizing it by the Carleman–Vekua method, we find the solution in an explicit form.

References

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Салахитдинов М.С. Нелокальные задачи для уравнений смешанного типа с сингулярными коэффициентами: монография / М.С. Салахитдинов, М. Мирсабуров. – Ташкент: Университет, 2005.

Ruziev M. Tricomi type equations with terms of lower order. / M. Ruziev, M. Reissig // Journal of Dynamical Systems and Differential Equations. 2016. Vol. 6. № 1. P. 14. DOI: https://doi.org/10.1504/IJDSDE.2016.074572

Мусхелишвили Н.И. Сингулярные интегральные уравнения: Граничные задачи теории функций и некоторые их приложения к математической физике: монография / Мусхелишвили Н.И. – Москва: Наука, 1968. - 511 с.

Published

2023-12-30

How to Cite

Ruziev, M., & Yuldasheva, N. (2023). THE BITSADZE–SAMARSKY TYPE PROBLEM FOR A MIXED-TYPE EQUATION WITH SINGULAR COEFFICIENTS: THE BITSADZE–SAMARSKY TYPE PROBLEM FOR A MIXED-TYPE EQUATION WITH SINGULAR COEFFICIENTS. Journal of Osh State University. Mathematics. Physics. Technical Sciences, (2(3), 115–124. https://doi.org/10.52754/16948645_2023_2_115