The paper is concerned with a qualitative analysis for a nonlinear second-order parabolic problem, subject to non-homogeneous Cauchy-Stefan-Boltzmann boundary conditions, extending the types already studied. Under certain assumptions, we prove the existence, a priori estimates, regularity and uniqueness of a solution in the class W 1,2 p (Q). Here we extend the results already proven by the authors for a nonlinearity of cubic type, making the present mathematical model to be more capable for describing the complexity of certain wide classes of real physical phenomena (phase separation and transition, for instance).

The existence, the estimate, and the uniqueness of a solution to a general phase-field system, motivated by Caginalp's model describing the phase changes, are established. The paper extends the results for the already studied types of nonlinearities related to the model. ᮊ

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