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Continuum theory of thermally induced phase transitions based on an order parameter. (English) Zbl 0793.35049
Summary: Using balance laws for accretive force and energy in conjunction with constitute equations restricted so as to be compatible with the second law, we develop a theory for the study of solid-liquid and solid-solid phase transitions where accretion and heat conduction dominate mass diffusion and deformation. Our theory furnishes generalizations of the Ginzburg-Landau equation and the phase-field equations, generalizations that allow for anisotropically induced preferred growth and nonlinear transition kinetics.

MSC:
35K40 Second-order parabolic systems
35K55 Nonlinear parabolic equations
80A22 Stefan problems, phase changes, etc.
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