Geodesic
On phase-field equations of Penrose-Fife type withthe non-conserved order parameter under flux boundary condition.I: Global-in-time solvability
Matematičeskie zametki SVFU, Tome 29 (2022) no. 1, pp. 103-121 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the initial-boundary value problem for the non-conserved phase-field model proposed by Penrose and Fife in 1990 [1] under the flux boundary condition for the temperature field in higher space dimensions, which is obliged to overcome additional di culties in the mathematical treatment. In all the existing works concerning this problem, only one due to Horn et al. [2] was discussed under the correct form of the flux boundary condition. Here we prove that the same correctly formulated problem as theirs is well-posed globally-in-time in Sobolev-Slobodetski spaces. Moreover, it is shown that the temperature keeps positive through the time evolution.
Keywords: non-conserved phase-field equations, Penrose–Fife type, flux boundary condition, strong solution in Sobolev–Slobodetskiĭ spaces. 
@article{SVFU_2022_29_1_a7,
     author = {A. Tani},
     title = {On phase-field equations of {Penrose-Fife} type withthe non-conserved order parameter under flux boundary {condition.I:} {Global-in-time} solvability},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {103--121},
     year = {2022},
     volume = {29},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2022_29_1_a7/}
}
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A. Tani. On phase-field equations of Penrose-Fife type withthe non-conserved order parameter under flux boundary condition.I: Global-in-time solvability. Matematičeskie zametki SVFU, Tome 29 (2022) no. 1, pp. 103-121. http://geodesic.mathdoc.fr/item/SVFU_2022_29_1_a7/