The Stochastic Viscous Cahn–Hilliard Equation: Well-Posedness, Regularity and Vanishing Viscosity Limit

被引：0
作者：
Luca Scarpa
机构：
[1] University of Vienna,Faculty of Mathematics
来源：
Applied Mathematics & Optimization | 2021年 / 84卷
关键词：
Stochastic viscous Cahn–Hilliard equation; Singular potential; Well-posedness; Regularity; Vanishing viscosity; Variational approach; 35K25; 35R60; 60H15; 80A22;
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学科分类号：
摘要：
Well-posedness is proved for the stochastic viscous Cahn–Hilliard equation with homogeneous Neumann boundary conditions and Wiener multiplicative noise. The double-well potential is allowed to have any growth at infinity (in particular, also super-polynomial) provided that it is everywhere defined on the real line. A vanishing viscosity argument is carried out and the convergence of the solutions to the ones of the pure Cahn–Hilliard equation is shown. Some refined regularity results are also deduced for both the viscous and the non-viscous case.
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页码：487 / 533
页数：46
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