Well-posedness for solid-liquid phase transitions with a fourth-order nonlinearity

[摘要] A phase-field system which describes the evolution of both the absolute temperature theta and the phase variable f during first-order transitions in thermal insulators is considered. A thermodynamic approach is developed by regarding the order parameter as a phase field and its evolution equation as a balance law. By virtue of the special form of the internal energy, a third-order nonlinearity G'(2) (f) appears in the energy balance in place of the (customarily constant) latent heat. As a consequence, the bounds 0 <= f <= 1 hold whenever theta is positive valued. In addition, a nonlinear Fourier law with conductivity proportional to temperature is assumed. Well-posedness for the resulting initial and boundary value problem are then established in a suitable setting. (C) 2007 Elsevier B.V. All rights reserved.

[发布日期] 2007-12-01

[关键词] phase transition;phase-field models;continuum thermodynamics;existence and uniqueness