Asymptotic behaviour of solutions to non-isothermal phase separation model with constraint in one-dimensional space

摘要

The above system arises in the phase separation of a binary mixture with components A and B. In this context, θ := ρ(u) represents the absolute temperature and w := w_a the order parameter which is the local concentration of the component A; note that σ_* = 0 ≤ W_A(t,x) ≤ 1 = σ~*, and w_A(t,x) = 1 (resp. w_A(t,x) = 0) means that the phase (the physical situation of the system) at (t,x) is of pure A (resp. pure B), while 0 < w_A(t, x) < 1 means that the phase at (t,x) is of mixture.