Abstract. We study a linear parabolic system in a domain with a thin low-permeable insertion. A new formulation of the problem is obtained with the unknowns (u, ω). Under this approach, the main second-order parabolic equation is converted to a set of first-order partial differential equations with distributional coefficients. The relations of the approach to the classical and weak formulations of the problem are analyzed.

Keywords: parabolic equation, discontinuous solution, transmission conditions, generalized functions.