Subdifferential Operator Approach to the Cahn-Hilliard Equation with Constraint

Nonlinear evolution inclusions arising from phase change models

“…There is nothing to prove if η = 0; otherwise we put [19]. There, the authors devise an argument leading to an a priori estimate for the V 0 -component of the solution u(t) to the Cahn-Hilliard equation with constraint (see [19,Lemma 5.2]).…”

“…There, the authors devise an argument leading to an a priori estimate for the V 0 -component of the solution u(t) to the Cahn-Hilliard equation with constraint (see [19,Lemma 5.2]). In Theorem 2.14 below we show a counterpart of this technique adapted to our situation.…”

“…In our abstract setting, the null-space of A is allowed to have an arbitrary finite dimension, while in [4], [14] or, e.g., [19], it is one-dimensional. We state sufficient conditions on A, B and Φ which ensure the existence and/or uniqueness of solutions to (1.1) for a suitable class of data.…”

A Cahn–Hilliard model in bounded domains with permeable walls

“…For the Cauchy problem (1) and (2) with the boundary conditions (3) and (4), the results on global existence, uniqueness and large time behaviour of solutions have been established in literature (see References [4][5][6][7][8], etc. ).…”

On the 2D Cahn–Hilliard Equation with Inertial Term

“…Here we recall, in particular, well-posedness for different boundary conditions and/or singular potentials, asymptotic behavior of solutions, existence of global and exponential attractors, analysis of the stationary states. We confine ourselves to quote only some contributions, namely, [4,11,12,13,28,29,31,32,34,35,37,38,39,40,44,45,46,50,51,52,53,54].…”