Conservative stochastic Cahn–Hilliard equation with reflection
By Arnaud Debussche, L. Zambotti. 2006
72 citations recorded by the source corpus.
We consider a stochastic partial differential equation with reflection at 0 and with the constraint of conservation of the space average. The equation is driven by the derivative in space of a space-time white noise and contains a double Laplacian in the drift. Due to the lack of the maximum principle for the double Laplacian, the standard techniques based on the penalization method do not yield existence of a solution. We propose a method based on infinite dimensional integration by parts formulae, obtaining existence and uniqueness of a strong solution for all continuous nonnegative initial conditions and detailed information on the associated invariant measure and Dirichlet form.
Subfields: Computational Theory and Mathematics, Finance, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/f3a17e84d963a692afdfa7eda393a7bd18450714
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In Computational Theory and Mathematics
- Alain Miranville
- Laurence Cherfils
- Sergey Zelik
- Luigi Ambrosio
- Hao Wu
- Giuseppe Savar'e
- L. Zambotti
- Ciprian G. Gal
In Finance
In Materials Chemistry
- Alain Miranville
- Sergey Zelik
- Laurence Cherfils
- Hao Wu
- Giuseppe Savar'e
- Ciprian G. Gal
- Maurizio Grasselli
- Andrea Giorgini
Citations in the corpus
- The phase field method for geometric moving interfaces and their numerical approximations (2019, unknown): “Some recent works on modeling and PDE analyses in this direction can be found in [166, 420, 421, 249, 346, 18, 20, 134, 133, 122, 363] and the references therein.”
- The Cahn-Hilliard Equation with Logarithmic Potentials (2011, background): “We also mention the stochastic Cahn-Hilliard equation (also called the Cahn-Hilliard-Cook equation) which takes into account thermal fluctuations (see [59]; see also [17], [18], [20], [21], [43], [61], [64], [75], [123] and [131]).”
- Existence and stability for Fokker–Planck equations with log-concave reference measure (2007, background): “6), have also been studied: see [24], [33], [34], [11].”