The phase-field transition system with non-homogeneous Cauchy–Stefan–Boltzmann and homogeneous Neumann boundary conditions and non-constant thermal conductivity

The paper establishes the existence, estimate, uniqueness and regularity for the solution of a nonlinear parabolic system (a two-phase Caginalp type system) with non-homogeneous Cauchy–Stefan–Boltzmann and homogeneous Neumann boundary conditions and non-constant thermal conductivity. It extends the already studied types of boundary conditions which makes the mathematical model to be richer and more flexible to describe the real physical phenomena, including phase separation.