Well-posedness for a phase-field transition system endowed with a polynomial nonlinearity and a general class of nonlinear dynamic boundary conditions

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This work is devoted to the study of a phase-field transition system of Caginalp type endowed with a general polynomial nonlinearity and a general class of nonlinear and nonhomogeneous dynamic boundary conditions (in both unknown functions). The existence, uniqueness and regularity of solutions are established. Here we extend several results proved by some authors, including the already studied boundary conditions, which makes the present mathematical model capable of revealing the complexity of a wide class of physical phenomena (for instance, phase change in Ω at the boundary of Ω).