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Abstract approach to evolution equations of phase-field type and applications. (English) Zbl 0978.35075
In this extended paper the author is concerned with the nonlinear parabolic equations that relate to the phase-field models of heat transfer in anisotropic fluids with phase transitions. An abstract approach is chosen, and general results on existence and uniqueness are proven.
In the second part of the article (Section 5) the results are applied to two physical situations: firstly, a heat diffusion problem, showing how existence and uniqueness results can be obtained from the previously proven theory and, secondly, a far more interesting problem, dealing with the heat and phase-field diffusion problem between two adjoining regions filled with fluids of possibly different physical characteristics. Finally, suggestions for possible expansions are included together with an open question.

MSC:
35Q72 Other PDE from mechanics (MSC2000)
35K90 Abstract parabolic equations
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