On Solvability of Conjugation Problems with Non-Ideal Contact Conditions

Abstract

In this paper, we study the regular solvability (in Sobolev spaces) of transmission problems for parabolic second-order systems with conjugation conditions of non-ideal contact type. The solution of such a problem has all generalized derivatives entering in the equation that are summable with some power $p\in (1,\infty)$ . One can express limit values of conormal derivatives at the interface in terms of combinations of limit values of the solution. This problem, arising when describing heat and mass transfer processes, differs from the classical statement of diffraction problems. The proof relies on derived a priori estimates and on the method of continuation in a parameter.