Nonlocal combined problem of Bitsadze–Samarski and Samarski–Ionkin type for a system of pseudoparabolic equations

We consider a boundary value problem for a fourth order system of pseudoparabolic equations with discontinuous coefficients and with conditions Bicadze–Samarsky and Samarsky–Ionkin. We find integral representation for a functions in the Sobolev space, which allows one to recover it through the values of certain operators (defining operators), taken at the function. We also justify formulation of the Goursat problem with nonclassical boundary conditions.