ON FRANKL'S PROBLEM FOR A MIXED-TYPE EQUATION WITH A SINGULAR COEFFICIENT
Keywords:
Regular operator, hypergeometric function, integral, Boltz formula, Wiener-Hopf equationAbstract
The paper considers a problem with the Frankl condition on different parts of
the cut edges along a segment of the degeneracy line for a mixed-type equation with a singular
coefficient. The problem is investigated TF in the case / 2 1 0 -m < b < of , uniqueness of the
solution of the problem TF and the existence of a solution TF to the singular Tricomi integral
equation is proved.
References
1. Nakhushev A.M. On some boundary value problems for hyperbolic and mixed-type
equations. // Differential equations. -1969. - vol. 5. - No. 1. - pp. 44-59.
2. Salakhitdinov M. S., Mirsaburov M. A problem with a non-local boundary condition on a
characteristic for one class of mixed-type equations. // Mathematical notes. -2009. - T. 86. -
No. 5. - pp. 748-760.
3. Salakhitdinov M. S., Urinov A. K. Boundary value problems for mixed-type equations with a
spectral parameter. Tashkent: Fan. -1997. - p. 165.
4. Babenko K. I. On the theory of mixed-type equations. Doctoral dissertation (Library of the
Steklov Mathematical Institute of the Russian Academy of Sciences), -1952.1952.
5. Bitsadze A.V. Equations of mixed type. // Publishing House of the USSR Academy of
Sciences, Moscow. 1959 – - p. 164.
6. Polosin A. A. On the unique solvability of the Tricomi problem for one special domain. //
Differential equations. -1996. - vol. 32. - No. 3. - pp. 394-401.
7. Ashurov R.R., Zunnunov R.T. An Analog of the Tricomi Problem for a Mixed-Type
Equation with Fractional Derivative. Inverse Problems // Lobachevskii journal of
mathematics, Vol. 44 No. 8, 2023. P.3225-3240.
8. Smirnov M. M. Equations of mixed type. Moscow: Nauka. -1970. - p. 296.
9. Smirnov M. M. Equations of mixed type. Moscow: Vysshaya shkola. -1985. - p. 304.
10.Weinstein A.Оn the wave equation and the equation Euler-Poisson. TheFifht symposium in
Applied Math. Macbaw-Hill-York. -1954. -pp.137-147.
11.Karatoprakliev G. On a generalization of the Tricomi problem. //Dokl. ACADEMY OF
SCIENCES OF THE USSR. -1964. - vol. 158. - No. 2. - pp. 271-274.
