engleski

On the stochastic Cahn-Hillard equation

The stochastic Cahn-Hilliard equation is a particular case of the nonlinear Langevin equation and arises in the nonequilibrium dynamics of metastable states. The paper is concerned with two types of solutions to this equation. First, the authors prove the existence of weak statistical solutions, i.e. measures concentrated on a set of possible trajectories, the only assumption being the existence of third-order moments of initial data with respect to the Hilbert norm. Second, it is shown that under additional conditions the Cahn-Hilliard equation has a unique strong solution with some additional regularity properties. The most delicate part of the proof relies on some nontrivial a priori estimates.

Cahn-Hilliard; stochastic partial differential equation; statistical solution

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