Cahn–Hilliard equation - Wikipedia

The Cahn–Hilliard equation (after John W. Cahn and John E. Hilliard)[1] is an equation of mathematical physics which describes the process of phase separation, spinodal decomposition, by which the two components of a binary fluid spontaneously separate and form domains pure in each component. If 𝑐 is the concentration of the fluid, with 𝑐 = ± 1 indicating domains, then the equation is written as where 𝐷 is a diffusion coefficient with units of Length 2 / Time and 𝛾 gives the length of the transition regions between the domains. Here ∂ / ∂ 𝑡 is the partial time derivative and ∇ 2 is the Laplacian in 𝑛 dimensions. Additionally, the quantity 𝜇 = 𝑐 3 − 𝑐 − 𝛾 ∇ 2 𝑐 is identified as a chemical potential. Related to it is the Allen–Cahn equation, as well as the stochastic Allen–Cahn and the stochastic Cahn–Hilliard equations. Of interest to mathematicians is the existence of a unique solution of the Cahn–Hilliard equation, given by smooth initial data. The proof r

Cahn–Hilliard equation - Wikipedia Jump to content From Wikipedia, the free encyclopedia Description of phase separation The Cahn–Hilliard equation (after John W. Cahn and John E. Hilliard ) [ 1 ] is an equation of mathematical physics which describes the process of phase separation, spinodal decomposition , by which the two components of a binary fluid spontaneously separate and form domains pure in each component. If c {\displaystyle c} is the concentration of the fluid, with c = ± 1 {\displaystyle c=\pm 1} indicating both domains, then the equation is written as ∂ c ∂ t = D ∇ 2 ( c 3 − c −

related reading

• Chapman–Kolmogorov equation - Wikipediaen.wikipedia.org
• Helmholtz equationen.wikipedia.org
• A Feynman-Kac Approach for the Spatial Derivative of the Solution to the Wick Stochastic Heat Equation Driven by Time Homogeneous White Noisearxiv.org
• Navier–Stokes equationsen.wikipedia.org
• Stochastic Heat Equations with General Multiplicative Gaussian Noises: Hölder Continuity and Intermittencyarxiv.org
• [2008.13092] Fundamental Solution to 1D Degenerate Diffusion Equation with Locally Bounded Coefficientsarxiv.org
• Hamilton-Jacobi Equationsmath.mcgill.ca
• Cauchy distribution - Wikipediaen.wikipedia.org
• On Degenerate Partial Differential Equationsarxiv.org
• Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditionsmath.emory.edu
• A Lecture on Partial Differential Equationspeople.math.harvard.edu
• theNotes.pdfweb.math.princeton.edu