Geodesic
A boundary value problem for mixed type equation with singular coefficient
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 35 (2021) no. 2, pp. 27-39 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we study a boundary value problem for a mixed type equation in a domain whose elliptic part is the first quadrant of the plane and the hyperbolic part is the characteristic triangle. With the help of the method of integral equations and the principle of extremum we prove the unique solvability of the considered problem
Keywords: rinciple of extremum, unique solvability, solvability, index of equation, integral equations.
Mots-clés : singular coefficient 
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M. Kh. Ruziev; F. S. Aktamov. A boundary value problem for mixed type equation with singular coefficient. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 35 (2021) no. 2, pp. 27-39. http://geodesic.mathdoc.fr/item/VKAM_2021_35_2_a2/

[1] Smirnov M.M., Mixed type equations, Higher school, Moscow, 1985, 304 pp. | MR

[2] Repin O. A., Kumykova S. K., “On a boundary value problem with shift for an equation of mixed type in an unbounded domain”, Differ. Equations, 48:8 (2012), 1127-1136 | Zbl

[3] Ruziev M. Kh., “Boundary value problem for the equation of mixed type with singular coefficient in the domain where the elliptic part is a half-band”, Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 18:1(18) (2009), 33-40 | Zbl

[4] Gellerstedt S., “Quelques problemes mixtes pour l$`$equation $y^{m}z_{xx}+z_{yy}=0$”, Ark. Math. Astron. Fys., 26A:3 (1938), 1–32

[5] Ruziev M. Kh., “A nonlocal problem for a mixed-type equation with a singular coefficient in an unbounded domain”, Russian Mathematics, 2010, no. 54, 36-43

[6] Mirsaburov M, Ruziev M. Kh., “A boundary value problem for a class of mixed type equations in an unbounded domain”, Differ. Equations, 47:1 (2011), 111-118 | MR | Zbl

[7] Lerner M. E., Pul'kin S. P., “On uniquness of solutions of problems satisfying the Frankl and Tricomi conditions for the general Lavrent'ev-Bitsadze equation”, Differ. Equations, 2:9 (1966), 1255-1263

[8] Bitsadze A. V., Some Classes of Partial Differential Equations, Science, Moscow, 1981, 448 pp.

[9] Gakhov F. D., Chersky Yu. I., Convolution type equations, Science, Moscow, 1978, 295 pp. | MR