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| {{\bf Abstract.}
The work is devoted to the study of a Caginalp phase-field transition system,
endowed with a general regular potential and a general class of nonlinear and
non-homogeneous dynamic boundary conditions (in both unknown functions), as well
as non-constant thermal conductivity.
The existence, uniqueness and regularity of solutions is established.
This extends previous works, including the already studied boundary conditions,
which makes the preset mathematical model capable to reveal
the complexity of the real physical phenomena, including the phase change.}
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\item {~~}{{\bf Key words.} Nonlinear initial-boundary value problems,
nonlinear parabolic systems, dynamic boundary conditions, Leray-Schauder principle,
Nemytskij's operator, thermodynamics, phase-field models.}
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\item {~~}{{\bf Subject classification.} 35B65, 35K61, 35Q56, 47H30, 74A15, 80A22.} |
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