On a boundary value problem for a third-order parabolic-hyperbolic type equation

Zh. A. Balkizov

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 2, pp. 211-225.

Résumé

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.

Détail

Keywords: degenerate hyperbolic equation, equation with multiple characteristics, parabolic-hyperbolic equation of third order, problems with a shift.

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