Regularity conditions for solutions to some parabolic systems

TL;DR

This paper studies the regularity of solutions to certain parabolic systems, establishing conditions under which solutions are smooth or classical, based on the properties of the data in generalized Sobolev spaces.

Contribution

It introduces new regularity conditions for solutions to Petrovskii parabolic systems, linking data spaces to solution smoothness.

Findings

Conditions for solutions to be classical are identified.

Regularity results depend on the Sobolev space properties of the data.

Both local and global regularity criteria are provided.

Abstract

We investigate global and local regularity of generalized solutions to parabolic initial-boundary value problem for Petrovskii system of second order differential equations. Results are formulated in terms of the belonging of right-hand sides of the problem to some generalized Sobolev spaces. We also obtain new sufficient conditions under which the generalized solution should be classical.