Geodesic
On a boundary value problem for a third-order parabolic-hyperbolic type equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 2, pp. 211-225

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In the article, we investigate a boundary-value problem with a third-order inhomogeneous parabolic-hyperbolic equation with a wave operator in a hyperbolicity domain. A linear combination with variable coefficients in terms of derivatives of the sought function on independent characteristics, as well as on the line of type and order changing is specified as a boundary condition. We have established necessary and sufficient conditions that guarantee existence and uniqueness of a regular solution to the problem under study. In some cases, a solution representation is written out explicitly.
Keywords: degenerate hyperbolic equation, equation with multiple characteristics, parabolic-hyperbolic equation of third order, problems with a shift. 
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     author = {Zh. A. Balkizov},
     title = {On a boundary value problem for a third-order parabolic-hyperbolic type equation},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {211--225},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2020_24_2_a0/}
}
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Zh. A. Balkizov. On a boundary value problem for a third-order parabolic-hyperbolic type equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 2, pp. 211-225. http://geodesic.mathdoc.fr/item/VSGTU_2020_24_2_a0/