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# A condition for generalized solutions of a parabolic problem for a Petrovskii system to be classical

### Abstract

We 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.

Key words: Parabolic problem, Hörmander space, slowly varying function, generalized solution, classical solution.

### Article Information

 Title A condition for generalized solutions of a parabolic problem for a Petrovskii system to be classical Source Methods Funct. Anal. Topology, Vol. 26 (2020), no. 2, 111-118 DOI 10.31392/MFAT-npu26_2.2020.03 MathSciNet MR4127608 Milestones Received 18.05.2020 Copyright The Author(s) 2020 (CC BY-SA)

### Authors Information

Valerii Los
National Technical University of Ukraine Igor Sikorsky Kyiv Polytechnic Institute, Prospect Peremohy 37, 03056, Kyiv-56, Ukraine

### Citation Example

Valerii Los, A condition for generalized solutions of a parabolic problem for a Petrovskii system to be classical, Methods Funct. Anal. Topology 26 (2020), no. 2, 111-118.

### BibTex

@article {MFAT1343,
AUTHOR = {Valerii Los},
TITLE = {A condition for generalized solutions of a parabolic problem for a Petrovskii system to be classical},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {26},
YEAR = {2020},
NUMBER = {2},
PAGES = {111-118},
ISSN = {1029-3531},
MRNUMBER = {MR4127608},
DOI = {10.31392/MFAT-npu26_2.2020.03},
URL = {http://mfat.imath.kiev.ua/article/?id=1343},
}

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