Antonopoulou, Dimitra C.; Karali, Georgia D.; Kossioris, Georgios T. Asymptotics for a generalized Cahn-Hilliard equation with forcing terms. (English) Zbl 1222.35017 Discrete Contin. Dyn. Syst. 30, No. 4, 1037-1054 (2011). Summary: Motivated by the physical theory of critical dynamics the Cahn-Hilliard equation on a bounded space domain is considered and forcing terms of general type are introduced. For such a rescaled equation the limiting inter-face problem is studied and the following are derived: (i) asymptotic results indicating that the forcing terms may slow down the equilibrium locally or globally, (ii) the sharp interface limit problem in the multidimensional case demonstrating a local influence in phase transitions of terms that stem from the chemical potential, while free energy independent terms act on the rest of the domain, (iii) a limiting non-homogeneous linear diffusion equation for the one-dimensional problem in the case of deterministic forcing term that follows the white noise scaling. Cited in 4 Documents MSC: 35B25 Singular perturbations in context of PDEs 35K58 Semilinear parabolic equations 35K35 Initial-boundary value problems for higher-order parabolic equations Keywords:Hele-Shaw problem; limiting inter-face problem; deterministic forcing; white noise scaling PDFBibTeX XMLCite \textit{D. C. Antonopoulou} et al., Discrete Contin. Dyn. Syst. 30, No. 4, 1037--1054 (2011; Zbl 1222.35017) Full Text: DOI