On a problem of the Frankl type for an equation of the mixed parabolic-hyperbolic type

Tynysbek Sh. Kalmenov, Makhmud Abdysametovich Sadybekov

2016

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DOI 10.1063/1.4959615
Data confidence 85 high
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Abstract

In the paper a new non-local boundary value problem for an equation of the parabolic-hyperbolic type is formulated. This equation is of the first kind, that is, the line of type change is not a characteristic of the equation. The suggested new nonlocal condition binds points on boundaries of the parabolic and hyperbolic parts of the domain with each other. This problem is generalization of the well-known problems of Frankl type. Unlike the existing publications of the other authors related to the theme, in the suggested formulation of the problem the hyperbolic part of the domain coincides with a characteristic triangle. Unique solvability of the formulated problem is proved in the sense of classical and strong solutions.