Boundary value problem for a parabolic-hyperbolic equation with a nonlocal integral condition

For a parabolic-hyperbolic equation with the heat and wave operators in a rectangular domain, we consider a problem with a nonlocal Samarksii-Ionkin condition. A criterion for the uniqueness of the solution is established by the spectral expansion method. The classical solution of the problem is constructed in the form of the sum of a biorthogonal series. The solution is proved to be stable with respect to the initial condition.

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