A nonlocal stochastic Cahn–Hilliard equation. (July 2016)

• Record Type: Journal Article
• Authors: Cornalba, Federico
• Is Part Of: Nonlinear analysis. Volume 140(2016)
• Page Start: 38
• Page End: 60
• Publication Date: 2016-07
• Subjects: 60H15 (35R60); Cahn–Hilliard -- Stochastic partial differential equation -- Variational solution; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.03.009
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a stochastic extension of the nonlocal convective Cahn–Hilliard equation containing an additive Wiener process noise. We first introduce a suitable analytical setting and make some mathematical and physical assumptions. We then establish, in a variational context, the existence of a weak statistical solution for this problem. Finally we prove existence and uniqueness of a strong solution .