Stochastic Cahn-Hilliard equation

DOI10.1016/0362-546X(94)00277-OzbMath0838.60056OpenAlexW2059086491MaRDI QIDQ4861553

Arnaud Debussche, Giuseppe Da Prato

Publication date: 12 February 1996

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(94)00277-o

zbMATH Keywords

Wiener processLaplace operatorCahn-Hilliard equationspace-time white noiseexistence and uniqueness of a solutionexistence and uniqueness of an invariant measure

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

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Cites Work

• Unnamed Item
• Unnamed Item
• Strong Feller property and irreducibility for diffusions on Hilbert spaces
• Some global dynamical properties of a class of pattern formation equations
• Ergodic Properties of Recurrent Diffusion Processes and Stabilization of the Solution to the Cauchy Problem for Parabolic Equations
• On the stochastic Cahn-Hilliard equation
• On the Cahn-Hilliard equation with a logarithmic free energy
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• Stochastic Equations in Infinite Dimensions