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

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 o...

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Bibliographic Details
Published in:Applied mathematics & optimization 2021-08, Vol.84 (1), p.487-533
Main Author: Scarpa, Luca
Format: Article
Language:English
Subjects:
Boundary conditions
Calculus of Variations and Optimal Control
Optimization
Control
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Polynomials
Regularity
Simulation
Systems Theory
Theoretical
Viscosity
Well posed problems
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Summary: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.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-020-09652-9