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Mathematical notes of NEFU, 2022, Volume 29, Issue 2, Pages 88–100
DOI: https://doi.org/10.25587/SVFU.2022.49.45.008 (Mi svfu353) 		 
Mathematics

On phase-field equations of Penrose-Fife type with non-conserved order parameter under flux boundary condition. II: Uniform boundedness

A. Tani

Department of Mathematics, Faculty of Science and Technology, Keio University
Full-text PDF (283 kB)
DOI: https://doi.org/10.25587/SVFU.2022.49.45.008
Abstract: In [1] we showed the global-in-time solvability of the initial-boundary value problem for the non-conserved phase-field model proposed by Penrose and Fife [2, 3] under the correct form of flux boundary condition for the temperature field in higher space dimensions. In this paper we discuss the uniform boundedness up to the infinite time of its solution in Sobolev-Slobodetskiĭ spaces.
Keywords: non-conserved phase-field equations, Penrose–Fife type, flux boundary condition, uniform boundedness of strong solution in Sobolev–Slobodetskiĭ spaces.
Received: 04.04.2021
Accepted: 31.05.2022
Document Type: Article
UDC: 517.95
Language: Russian
Citation: A. Tani, “On phase-field equations of Penrose-Fife type with non-conserved order parameter under flux boundary condition. II: Uniform boundedness”, Mathematical notes of NEFU, 29:2 (2022), 88–100
Citation in format AMSBIB
\Bibitem{Tan22}
\by A.~Tani
\paper On phase-field equations of Penrose-Fife type with non-conserved order parameter under flux boundary condition. II: Uniform boundedness
\jour Mathematical notes of NEFU
\yr 2022
\vol 29
\issue 2
\pages 88--100
\mathnet{http://mi.mathnet.ru/svfu353}
\crossref{https://doi.org/10.25587/SVFU.2022.49.45.008}
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