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

TL;DR

This paper establishes a new sufficient condition involving anisotropic H"ormander spaces that ensures generalized solutions to a parabolic Petrovskii system are classical, enhancing understanding of solution regularity.

Contribution

It introduces a novel condition based on anisotropic H"ormander spaces that guarantees classical solutions for a parabolic Petrovskii system.

Findings

New sufficient condition for classical solutions

Condition formulated via anisotropic H"ormander spaces

Applicable to homogeneous Cauchy data

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 H\"ormander spaces.