Simultaneous Identification of Two Time Independent Coefficients in a Nonlinear Phase Field System: Advancements in the study of phase field models and their applications (Journal of Advances and Scholarly Researches in Allied Education, 2018)
In the mathematical literature, the free boundary problems arising from phase transitions have been studied for over a century. Most of the work is concerned with the classical Stefan problem which incorporates the physics of latent heat and heat diffusion in a homogeneous medium. It should be recalled that the phase field models were first introduced and recently several authors redis-cussed the problem and also improved the results from the thermo dynamical point of view see, for instance, the work for an exhaustive explanation of the underlying physics and in fact these works provide an extension of the enthalpy method for the Stefan problem with the advantage of making it possible to describe some rather fine physical phenomena which can take place during fusion-solidification processes. Moreover, in the recent years, the study of several variants of the model has been done and interesting results have been obtained in the directions of existence and regularity of solutions as well as of their dependence on the physical parameters and one can see and for the dynamical controllability of phase field models with one and two control forces respectively.