How Do Degenerate Mobilities Determine Singularity Formation in Cahn--Hilliard Equations?
From MaRDI portal
Publication:5006471
DOI10.1137/21M1391249zbMath1471.35006arXiv2101.05116MaRDI QIDQ5006471
Publication date: 16 August 2021
Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2101.05116
matched asymptotic expansionslubrication theoryphase-field modelssharp interfacedegenerate fourth order partial differential equations
Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for higher-order parabolic equations (35K35) Dynamics of phase boundaries in solids (74N20) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Nonlinear higher-order PDEs (35G20) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26) Singularity in context of PDEs (35A21) Semilinear parabolic equations (35K58)
Related Items (3)
A multiphase Cahn–Hilliard system with mobilities and the numerical simulation of dewetting ⋮ A structure-preserving, upwind-SAV scheme for the degenerate Cahn-Hilliard equation with applications to simulating surface diffusion ⋮ A uniquely solvable, positivity-preserving and unconditionally energy stable numerical scheme for the functionalized Cahn-Hilliard equation with logarithmic potential
Cites Work
- Unnamed Item
- Unnamed Item
- Toward predictive multiscale modeling of vascular tumor growth, computational and experimental oncology for tumor prediction
- The thin film equation with backwards second order diffusion
- Higher order nonlinear degenerate parabolic equations
- Thin-film rupture for large slip
- Dynamics of three-dimensional thin film rupture
- Nonnegativity preserving convergent schemes for the thin film equation
- Finite-time thin film rupture driven by modified evaporative loss
- Isogeometric analysis of the Navier-Stokes-Cahn-Hilliard equations with application to incompressible two-phase flows
- Convergence of the Cahn-Hilliard equation to the Hele-Shaw model
- Nonnegative solutions of a fourth-order nonlinear degenerate parabolic equation
- Linking anisotropic sharp and diffuse surface motion laws via gradient flows
- Existence for an Allen-Cahn/Cahn-Hilliard system with degenerate mobility
- On singularity formation in a Hele-Shaw model
- Selection and validation of predictive models of radiation effects on tumor growth based on noninvasive imaging data
- Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching
- Computational studies of coarsening rates for the Cahn-Hilliard equation with phase-dependent diffusion mobility
- Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy
- Diffuse interface model for incompressible two-phase flows with large density ratios
- A phase field model for the electromigration of intergranular voids
- Surface evolution of elastically stressed films under deposition by a diffuse interface model
- Symmetry and self-similarity in rupture and pinchoff: a geometric bifurcation
- Moving boundary problems and non-uniqueness for the thin film equation
- Sharp-Interface Limits of the Cahn--Hilliard Equation with Degenerate Mobility
- Unifying binary fluid diffuse-interface models in the sharp-interface limit
- THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES
- Self-similar rupture of viscous thin films in the strong-slip regime
- Study of a three component Cahn-Hilliard flow model
- Dynamics of fluctuations and spinodal decomposition in polymer blends
- Front migration in the nonlinear Cahn-Hilliard equation
- Rupture of thin viscous films by van der Waals forces: Evolution and self-similarity
- A new phase-field model for strongly anisotropic systems
- Long-wave instabilities and saturation in thin film equations
- Nonlinear rupture of free films
- On the motion of a small viscous droplet that wets a surface
- Convergence of solutions to cahn-hilliard equation
- The lubrication approximation for thin viscous films: the moving contact line with a 'porous media' cut-off of van der Waals interactions
- The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation
- Stable and unstable singularities in the unforced Hele-Shaw cell
- Finite Element Approximation of a Degenerate Allen--Cahn/Cahn--Hilliard System
- Finite Element Approximation of a Phase Field Model for Void Electromigration
- The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature
- Numerical and asymptotic results on the linear stability of a thin film spreading down a slope of small inclination
- The Motion with Slip of a Thin Viscous Droplet over a Solid Surface
- THE SPREADING OF A THIN DROP BY GRAVITY AND CAPILLARITY
- A diffuse interface approach to Hele Shaw flow
- Existence and uniqueness of radially symmetric stationary points within the gradient theory of phase transitions
- On the Cahn–Hilliard Equation with Degenerate Mobility
- Symmetric Singularity Formation in Lubrication-Type Equations for Interface Motion
- Motion of Interfaces Governed by the Cahn--Hilliard Equation with Highly Disparate Diffusion Mobility
- Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility
- Positivity-Preserving Numerical Schemes for Lubrication-Type Equations
- Emerging areas of mathematical modelling
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- Coarsening Mechanism for Systems Governed by the Cahn--Hilliard Equation with Degenerate Diffusion Mobility
- An anisotropic phase-field model for solid-state dewetting and its sharp-interface limit
- A diffuse-interface model for electrowetting drops in a Hele-Shaw cell
- Very Singular Solutions for Thin Film Equations with Absorption
- Weak solutions for the Cahn-Hilliard equation with degenerate mobility
This page was built for publication: How Do Degenerate Mobilities Determine Singularity Formation in Cahn--Hilliard Equations?
