Nucleation in the one-dimensional Cahn-Hilliard Model
In the first part we study the one-dimensional Cahn-Hilliard equation. The dynamics can be reduced to an inertial manifold. Using Conley index theory we study the fine structure of the global attractor. In particular we consider the basin of attraction D of the homogenuous solution. We show that the first spikes always lie on the boundary of D and minimize the free Ginzburg-Landau energy on this boundary. In the second part we introduce an additional stochastic noise term in the equation. Now solutions leave the domain D almost surely. We prove that the exit points are located near the first spikes with overwhelming probabiltity if the noise intensity is small. To some extend this describes the physical phenomenon of 'nucleation'.
info:eu-repo/classification/ddc/510, Cahn-Hilliard-Gleichung, Große Abweichung, Attraktor, Inertialmannigfaltigkeit, Conley-Index, Mathematik, Cahn-Hilliard-Cook Gleichung, Stochastische Cahn-Hilliard Gleichung, Prinzip der grossen Abweichung, Austritt aus einem Gebiet, Cahn-Hilliard equation, attractor, inertial manifold, Cahn-Hilliard-Cook equation, exit problem
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