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Cahn-Hilliard equation with capillarity in actual deforming configurations. (English) Zbl 1454.35378

Summary: The diffusion driven by the gradient of the chemical potential (by the Fick/Darcy law) in deforming continua at large strains is formulated in the reference configuration with both the Fick/Darcy law and the capillarity (i.e. concentration gradient) term considered at the actual configurations deforming in time. Static situations are analysed by the direct method. Evolution (dynamical) problems are treated by the Faedo-Galerkin method, the actual capillarity giving rise to various new terms as e.g. the Korteweg-like stress and analytical difficulties related to them. Some other models (namely plasticity at small elastic strains or damage) with gradients at an actual configuration allow for similar models and analysis.

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
37N15 Dynamical systems in solid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
74A30 Nonsimple materials
74H20 Existence of solutions of dynamical problems in solid mechanics
76S05 Flows in porous media; filtration; seepage
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