Regularity conditions for the solutions to some parabolic systems

  • O. V. Diachenko National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”
  • V. M. Los National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” https://orcid.org/0000-0002-3661-3090
Keywords: Parabolic initial-boundary value problem, generalized Sobolev space, generalized solution, local regularity, classical solution

Abstract

УДК 517.956.4

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.

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Published
04.10.2022
How to Cite
Diachenko, O. V., and V. M. Los. “Regularity Conditions for the Solutions to Some Parabolic Systems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 8, Oct. 2022, pp. 1107 -17, doi:10.37863/umzh.v74i8.7225.
Section
Research articles