The Bitsadze–Samarskii problem for a loaded hyperbolic-parabolic equation with degeneracy of order in the hyperbolicity domain

In this paper, we study the nonlocal Bitsadze–Samarskii-type problem with internal boundary conditions for a loaded hyperbolic-parabolic equation with order degeneracy in the hyperbolicity domain. These boundary conditions are a special case of Nakhushev's nonlocal condition. We find the condition for existence and uniqueness of a solution to the problem and obtain a representation of the solution in the parabolic part of the domain and the explicit solution in the hyperbolic part of the domain.