A Variational Approach to a Cahn–Hilliard Model in a Domain with Nonpermeable Walls
We deal with the well-posedness and the long time behavior of a Cahn–Hilliard model with a singular bulk potential and suitable dynamic boundary conditions. We assume that the system is confined in a vessel with nonpermeable walls and the total mass, in the bulk and on the boundary, is conserved. As a result, the well-posedness in the sense of distributions may not hold and new notions of solutions are required. The same problem has been analyzed, relying on duality techniques, under weak assumptions on the nonlinearities. We improve these results by introducing a variational formulation of the problem, based on a proper variational inequality. Bibliography: 26 titles.
KeywordsGlobal Attractor Variational Solution Singular Function Singular Potential Porous Media Equation
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