| Contents |
| {\bf Abstract.}~~
The paper concerns with the existence, uniqueness, regularity and the approximation of solutions to the nonlinear phase-field (Allen-Cahn) equation, endowed with
non-homogeneous dynamic boundary conditions (depending both on time and space variables). It extends the already studied types of boundary conditions,
which makes the problem to be more able to describe many important phenomena of two-phase systems, in particular, the interactions with the walls in confined systems.
The convergence and error estimate results for an iterative scheme of fractional steps type,
associated to the nonlinear parabolic equation, are also established.
The advantage of such method consists in simplifying the numerical computation.
On the basis of this approach, a conceptual numerical algorithm is formulated in the end.
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\item {~}{\it Key words.} boundary value problems for nonlinear parabolic PDE,
stability and convergence of numerical method, thermodynamics, heat transfer
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\item {~}{\it Subject classification.} 35K55, 65N12, 80AXX. |
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