The Stochastic Viscous Cahn–Hilliard Equation: Well-Posedness, Regularity and Vanishing Viscosity Limit
Luca Scarpa
Abstract
Abstract 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.
Topics & Concepts
Cahn–Hilliard equationMathematicsViscosityLimit (mathematics)Mathematical analysisInfinityViscosity solutionUniquenessNeumann boundary conditionViscous liquidBoundary (topology)PhysicsPartial differential equationThermodynamicsSolidification and crystal growth phenomenaAdvanced Mathematical Modeling in EngineeringStochastic processes and financial applications