2018
Том 70
№ 9

# Systems parabolic in Petrovskii's sense in Hörmander spaces

Los’ V. M.

Abstract

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.