Naslov
On the stochastic Cahn-Hillard equation

Autori
Elezović, Neven ; Mikelić, Andro

Izvornik
Nonlinear analysis, Theorz, Methods & Applications (0362-546X) 16 (1991), 12; 1169-1200

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Cahn-Hilliard; stochastic partial differential equation; statistical solution

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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