Boundary value problems for composite type equations with a quasiparabolic operator in the leading part having the variable direction of evolution and discontinuous coefficients

The solvability of boundary value problems for non-classical Sobolev type differential equations with an alternating function is studied. This function has a discontinuity of the first kind at the point zero and changes its sign depending on the sign of the variable $x$. The existence and uniqueness of regular solutions having generalized derivatives are proved. To this end we derived a priori estimates.