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Документ Відкритий доступ A condition for generalized solutions of a parabolic problem for a Petrovskii system to be classical(Institute of Mathematics NAS of Ukraine, 2020) Los, ValeriiWe obtain a new sufficient condition under which generalized solutions to a parabolic initial-boundary-value problem for a Petrovskii system and the homogeneous Cauchy data are classical. The condition is formulated in terms of the belonging of the right-hand sides of the problem to some anisotropic Hörmander spaces.Документ Відкритий доступ Initial-boundary value problems for two-dimensional parabolic equations in Hörmander spaces(Institute of Mathematics NAS of Ukraine, 2017) Los, ValeriiWe investigate a general nonhomogeneous initial-boundary value problem for a two-dimensional parabolic equation in some anisotropic Hörmander inner product spaces. We prove that the operators corresponding to this problem are isomorphisms between appropriate Hormander spaces.