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The dynamics of nucleation for the Cahn-Hilliard equation. (English) Zbl 0788.35061
The authors show a description of the dynamics of nucleation for the Cahn-Hilliard equation in one space dimension, discussing some of the fundamental mathematical issues related to this important event. They carry out their study in the case of an initial boundary value problem in one space dimension on a finite interval, assuming the equation of the form ${\partial u \over \partial t}={\partial^ 2 \over \partial x^ 2} \left(-\varepsilon^ 2 {\partial^ 2 \over \partial x^ 2} u+f(u) \right)$ with Neumann boundary conditions $$(\partial u/ \partial x=\partial^ 3 u/ \partial x^ 3=0)$$ at the endpoints of the interval.

##### MSC:
 35K35 Initial-boundary value problems for higher-order parabolic equations 35B25 Singular perturbations in context of PDEs 35B40 Asymptotic behavior of solutions to PDEs 82D20 Statistical mechanical studies of solids 35R35 Free boundary problems for PDEs 35Q72 Other PDE from mechanics (MSC2000) 82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
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