Siberian Federal University

We investigate the problem on Runge pairs for Sobolev solutions of strongly uniformly parabolic systems in non-cylindrical domains of a special kind. We prove that if the coefficients of a parabolic operator are constant, then two domains with sufficiently smooth boundaries, no parts of which are parallel to the plane t = 0, form a Runge pair if and only if the complements of any section of the larger domain to the section of the smaller domain by planes t = const, have no compact components in the larger section