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A mathematical model of dynamics of non-isothermal phase separation. (English) Zbl 0763.58031
The authors propose a mathematical model of phase separation that includes the description of coupled mass diffusion and heat conduction in binary systems under thermal activation. The model is an extension of the model constructed by J. W. Cahn and J. E. Hilliard [Acta Metall. 19, 151-161 (1971)] to the non-isothermal case. In constructing the extension use is made of the Landau-Ginzburg free energy functional and non-equilibrium thermodynamics. The model is described by a system of nonlinear parabolic differential equations for the concentration and the energy as the conserved quantities. The authors establish the existence of a Lyapunov functional that is non-increasing in time. In the one- dimensional case a finite-dimensional approximation complete with a method for its numerical solution is proposed.

MSC:
58Z05 Applications of global analysis to the sciences
82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
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