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Second phase spinodal decomposition for the Cahn-Hilliard-Cook equation. (English) Zbl 1130.60066
The authors consider a stochastic Cahn-Hilliard-Cook model. In a previous paper, the same authors proved that in this model the homogeneous state is no longer in equilibrium since the stochastic fluctuations drive the dynamics quickly away from the homogeneous state. In the present paper they study the spinodal decomposition in the Cahn-Hilliard-Cook model. They show that such decomposition is divided in two stages. First, the authors consider a general framework involving nonlinear semigroups in Hilbert spaces. They show that theses equations have basically linear dynamics far from equilibrium. In a first stage this is a consequence of the closeness of the solution to the homogeneous state. During a second stage it is due to sharp nonlinearity estimates in a region of phase space. Finally, these results are applied to a stochastic Cahn-Hilliard-Cook equation. They are used to explain spinodal decomposition which addresses the dynamics and the morphology of the observed patterns.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35K35 Initial-boundary value problems for higher-order parabolic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
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