On solvability of conjugation problems with non-ideal contact conditions

In the article we examine the questions of regular solvability in the Sobolev spaces of the transmission problems with transmission conditions of non-ideal contact type for parabolic second order systems. A solution has all generalized derivatives occurring in the system summable to some power $p\in (1,\infty)$. At the interface the limit values of the conormal derivatives are expressed trough the limit values of a solution. The problem does not belong to the class of classical diffraction problems and arises when describing heat-and-mass transfer processes. The proof relies on a priori bounds and the method of continuation in a parameter.