We study a general parabolic initial-boundary-value problem for systems parabolic in Petrovskii’s sense with zero initial
Cauchy data in some anisotropic H¨ormander inner-product spaces.We prove that the operators corresponding to this problem
are isomorphisms between the appropriate H¨ormander spaces. As an application of this result, we establish a theorem on
the local increase in regularity of solutions of the problem. We also obtain new sufficient conditions of continuity for the
generalized partial derivatives of a given order of a chosen component of the solution.
Citation Example:Los’ V. M. Systems parabolic in Petrovskii's sense in Hörmander spaces // Ukr. Mat. Zh. - 2017. - 69, № 3. - pp. 365-380.