On a Conserved Penrose-Fife Type System

Periodic solutions of non-isothermal phase separation models with constraint

“…We refer the reader, among a vast literature, to, e.g., [6,8,9,20,24,34]. As the non-isothermal phase separation model, the analogous version of (1.1) has also received much attention during the last decades, see [3,5,8,10,12,13,15,17,19,27,28] and the references therein.…”

“…We refer the reader, among a vast literature, to, e.g., [6,8,9,20,24,34]. As the non-isothermal phase separation model, the analogous version of (1.1) has also received much attention during the last decades, see [3,5,8,10,12,13,15,17,19,27,28] and the references therein. It is worth pointing out that in [5,8,13,17,19], as well as in the most of the literature on the subject, third boundary conditions for temperature θ or α(θ) is essential, the arguments therein are not applicable to the case of the homogeneous Neumann boundary condition [12,15] or Dirichlet boundary condition [10,27,28] and the more delicate analysis is needed.…”

“…As the non-isothermal phase separation model, the analogous version of (1.1) has also received much attention during the last decades, see [3,5,8,10,12,13,15,17,19,27,28] and the references therein. It is worth pointing out that in [5,8,13,17,19], as well as in the most of the literature on the subject, third boundary conditions for temperature θ or α(θ) is essential, the arguments therein are not applicable to the case of the homogeneous Neumann boundary condition [12,15] or Dirichlet boundary condition [10,27,28] and the more delicate analysis is needed. Moreover, the viscosity term −μΔw t (μ > 0) is included into the kinetic equation for the conserved order parameter, which plays an important role in obtaining the regularity w ∈ W 1,2 (0, T ; L 2 (Ω)), in the above mentioned papers except [12] where α(θ) = − 1 θ and the Neumann boundary condition is generally homogeneous.…”