Coerciveness of the discontinuous initial-boundary value problem for parabolic equations

In this paper, the mixed problem for parabolic equations is investigated with the discontinuous coefficient at the highest derivative and with nonstandard boundary conditions. Namely, the boundary conditions contain values of the solution not only on the boundary points, but also on the inner points of the considered domain as well. Moreover, abstract functionals are involved in the boundary conditions. We single out a class of functional spaces in which coercive solvability occurs for the investigated problem.