Regular Conditions for the Solutions to Some Parabolic Systems

We study the properties of global and local regularity of generalized solutions to the parabolic initial-boundary-value problem for the Petrovskii system of second-order differential equations. The results are formulated in terms of belonging of the right-hand sides of the problem to certain general...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2023, Vol.74 (8), p.1263-1274
Main Authors: Diachenko, O. V., Los, V. M.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Anisotropy
Applications of Mathematics
Boundary value problems
Differential equations
Geometry
Mathematics
Mathematics and Statistics
Sobolev space
Statistics
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Summary:We study the properties of global and local regularity of generalized solutions to the parabolic initial-boundary-value problem for the Petrovskii system of second-order differential equations. The results are formulated in terms of belonging of the right-hand sides of the problem to certain generalized Sobolev spaces. We also establish new sufficient conditions under which the generalized solution should be classical.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-023-02133-6