Initial-boundary value problem for a parabolic-hyperbolic equation with power-law degeneration on the type change line

We consider the first boundary value problem for equations of mixed type in a rectangular domain. A criterion for the solution uniqueness is proved by the spectral expansion method. The solution is constructed in the form of a series in the eigenfunctions of the corresponding one-dimensional spectral problem. The stability of the solution with respect to the initial function is proved.

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