Geodesic
On the solvability of boundary-value problems for third-order equations of parabolic-hyperbolic type with lower terms
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 210 (2022), pp. 12-23

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In this paper, boundary-value problems for a third-order mixed differential equation of the parabolic-hyperbolic type with a fractional Gerasimov–Caputo operator are examined. Classes of functions that ensure the unique solvability of the boundary-value problem are found. The existence and uniqueness of a solution of the boundary-value problem are proved.
Keywords: parabolic-hyperbolic equation, Gerasimov–Caputo differential operator, integral equation, uniqueness of solution
Mots-clés : existence of solution. 
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     author = {O. Kh. Abdullaev and A. A. Matchanova},
     title = {On the solvability of boundary-value problems for third-order equations of parabolic-hyperbolic type with lower terms},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {12--23},
     publisher = {mathdoc},
     volume = {210},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_210_a2/}
}
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O. Kh. Abdullaev; A. A. Matchanova. On the solvability of boundary-value problems for third-order equations of parabolic-hyperbolic type with lower terms. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 210 (2022), pp. 12-23. http://geodesic.mathdoc.fr/item/INTO_2022_210_a2/