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On the Cahn-Hilliard equation

https://doi.org/10.1007/bf00251803
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Outgoing claims: the papers this work cites, builds on, or argues with.

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Global, small amplitude solutions to nonlinear evolution equations
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Galerkin Finite Element Methods for Parabolic Problems
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Non-Homogeneous Boundary Value Problems and Applications
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Non-Homogeneous Boundary Value Problems and Applications
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Pattern Formation for a One Dimensional Evolution Equation Based on Thom’s River Basin Model.
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A generalized diffusion model for growth and dispersal in a population
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Structured phase transitions on a finite interval
inferredcites →https://doi.org/10.1016/0167-2789(83)90321-4openalex-snapshot
On cellular instability in the solidification of a dilute binary alloy
inferredcites →https://doi.org/10.1016/0167-2789(84)90180-5openalex-snapshot
Nonlinear aspects of the Cahn-Hilliard equation
inferredcites →https://doi.org/10.1016/b978-0-12-208350-1.50007-8openalex-snapshot
Some Convergence Results for Galerkin Methods for Parabolic Boundary Value Problems
inferredcites →https://doi.org/10.1063/1.1744102openalex-snapshot
Free Energy of a Nonuniform System. I. Interfacial Free Energy
inferredcites →https://doi.org/10.1090/qam/973383openalex-snapshot
Energy methods for the Cahn-Hilliard equation
inferredcites →https://doi.org/10.1090/s0025-5718-1975-0371077-0openalex-snapshot
Optimal 𝐿_{∞} error estimates for Galerkin approximations to solutions of two-point boundary value problems
inferredcites →https://doi.org/10.1137/0710062openalex-snapshot
A Priori $L_2 $ Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations
inferredcites →https://doi.org/10.1137/0712016openalex-snapshot
On Maximum Norm Error Estimates for Galerkin Approximations to One-Dimensional Second Order Parabolic Boundary Value Problems

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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A Novel Finite Difference-Spectral Method and its Error Analysis for Cahn-Hilliard Equation in Polar Geometry
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Invariant Sample Measures and Sample Statistical Solutions for Nonautonomous Stochastic Lattice Cahn-Hilliard Equation with Nonlinear Noise
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Cahn–Hilliard Equation
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Exponential attractors for a singularly perturbed Cahn‐Hilliard system
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Convergence to steady states of solutions of the Cahn–Hilliard and Caginalp equations with dynamic boundary conditions
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Computational analysis of spinodal decomposition dynamics in polymer solutions
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Classical solvability of 1‐D Cahn–Hilliard equation coupled with elasticity
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Finite difference approximate solutions for the Cahn‐Hilliard equation
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A numerical scheme for the solution of viscous Cahn–Hilliard equation
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Goal‐oriented error estimation for Cahn–Hilliard models of binary phase transition
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Error estimates of fully discrete finite element solutions for the 2D Cahn–Hilliard equation with infinite time horizon
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Numerical error analysis for nonsymmetric interior penalty discontinuous Galerkin method of Cahn–Hilliard equation
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Adaptive trust‐region POD for optimal control of the Cahn‐Hilliard equation
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Singular perturbation problem for steady state solutions to a model equation of phase separation
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On uniqueness results for an elliptic‐parabolic‐system of partial differential equations arising in dynamic electrowetting
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A Numerical Study of Electro-migration Voiding by Evolving Level Set Functions on a Fixed Cartesian Grid
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Maximal L p-regularity and Long-time Behaviour of the Non-isothermal Cahn-Hilliard Equation with Dynamic Boundary Conditions
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Analysis of a finite element formulation for modelling phase separation
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Isogeometric Analysis of Phase-Field Models: Application to the Cahn-Hilliard Equation
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Boundedness Estimates to a Steady State Nonlinear Fourth Order Elliptic Equation
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Long Time Behavior for Some Higher Order Partial Differential Equations
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Positive Steady State Solutions to a Nonlinear Fourth Order Elliptic Equation
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Equilibrium Phase Transition in Statistical Physics
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Geophysical Fluid Dynamics and Climate Dynamics
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New Phase-Field Models with Applications to Materials Genome Initiative
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Simulation and Control of a Nonsmooth Cahn–Hilliard Navier–Stokes System with Variable Fluid Densities
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The Conforming Virtual Element Method for Polyharmonic and Elastodynamics Problems: A Review
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Hyperbolic Relaxation of the Chemical Potential in the Viscous Cahn–Hilliard Equation
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Existence of Weak Solutions for a Diffuse Interface Model of Power-Law Type Two-Phase Flows
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Dynamics of Non-Isothermal Phase Separation
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On the Approximate Controllability for Higher Order Parabolic Nonlinear Equations of Cahn-Hilliard Type
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The Cahn-Hilliard Model for the Kinetics of Phase Separation
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A Boundary Control Problem for the Equation and Dynamic Boundary Condition of Cahn–Hilliard Type
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Limiting Problems for a Nonstandard Viscous Cahn–Hilliard System with Dynamic Boundary Conditions
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Some Recent Developments in Optimal Control of Multiphase Flows
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POD for Optimal Control of the Cahn-Hilliard System Using Spatially Adapted Snapshots
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Dynamics of Diffusive Phase Transitions Driven by Coupled Mechanisms
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Spectral Method
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Convergence of the Cahn-Hilliard equation to the Hele-Shaw model
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Existence for the Cahn-Hilliard phase separation model with a nondifferentiable energy
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Global behavior of the solutions of certain fourth-order nonlinear equations
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The dynamics of a two-component fluid in the presence of capillary forces
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Asymptotic solutions of the Cahn-Hilliard system in the fast relaxation case
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Passage to the limit over a small parameter in the cahn-hilliard equations
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Asymtotic behaviour of the viscous Cahn-Hilliard equation
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Finite element scheme for the viscous Cahn-Hilliard equation with a nonconstant gradient energy coefficient
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A discontinuous Galerkin method for the Cahn-Hilliard equation
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Viscosity approach to modelling non-isothermal diffusive phase separation
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A stable, convergent, conservative and linear finite difference scheme for the Cahn-Hilliard equation
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Systems of nonlinear PDEs arising from dynamical phase transitions
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A stable and conservative finite difference scheme for the Cahn-Hilliard equation
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A Cahn–Hilliard system with forward-backward dynamic boundary condition and non-smooth potentials
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Homogenization of Cahn–Hilliard-type equations via evolutionary $$\varvec{\Gamma }$$-convergence
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The Cahn-Hilliard Equation with Logarithmic Potentials
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Well-posedness and large time behavior for Cahn–Hilliard–Oono equation
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An Energetic Variational Approach for the Cahn–Hilliard Equation with Dynamic Boundary Condition: Model Derivation and Mathematical Analysis
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A gradient flow approach to relaxation rates for the multi-dimensional Cahn–Hilliard equation
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Error analysis of a mixed finite element method for the Cahn-Hilliard equation
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Numerical approximation of the Cahn-Larché equation
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Error control for the approximation of Allen–Cahn and Cahn–Hilliard equations with a logarithmic potential
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From Vlasov equation to degenerate nonlocal Cahn-Hilliard equation
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The biharmonic heat operator on edge manifolds and non-linear fourth order equations
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Optimal Control for the Convective Cahn–Hilliard Equation in 2D Case
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A Boundary Control Problem for the Viscous Cahn–Hilliard Equation with Dynamic Boundary Conditions
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On a Class of Conserved Phase Field Systems with a Maximal Monotone Perturbation
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Local Exact Controllability to the Trajectories of the Cahn–Hilliard Equation
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The Stochastic Viscous Cahn–Hilliard Equation: Well-Posedness, Regularity and Vanishing Viscosity Limit
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Optimality Conditions for Sparse Optimal Control of Viscous Cahn–Hilliard Systems with Logarithmic Potential
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Multi-species viscous models for tissue growth: incompressible limit and qualitative behaviour
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Phase Separation in the Advective Cahn–Hilliard Equation
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Analysis and Optimal Velocity Control of a Stochastic Convective Cahn–Hilliard Equation
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Existence for a Cahn–Hilliard Model for Lithium-Ion Batteries with Exponential Growth Boundary Conditions
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A staggered approach for the coupling of Cahn–Hilliard type diffusion and finite strain elasticity
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A novel energy-based modeling framework
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A Gamma-convergence approach to the Cahn–Hilliard equation
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Slow motion for the nonlocal Allen–Cahn equation in n dimensions
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Layer dynamics for the one dimensional $$\varvec{\varepsilon }$$-dependent Cahn–Hilliard/Allen–Cahn equation
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Smoothness and long time existence for solutions of the Cahn–Hilliard equation on manifolds with conical singularities
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Regularity of Solutions of the Cahn–Hilliard Equation with Non–constant Mobility
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One-dimensional viscous diffusion equation of higher order with gradient dependent potentials and sources
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Weak Solutions to the Cahn-Hilliard Equation with Degenerate Diffusion Mobility in ℝN
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Cahn–Hilliard equation with nonlocal singular free energies
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Global well-posedness of solutions to the Cauchy problem of convective Cahn–Hilliard equation
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On a Cahn–Hilliard system with convection and dynamic boundary conditions
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A class of stable and conservative finite difference schemes for the Cahn-Hilliard equation
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On the Existence of Global Attractor for 3D Viscous Cahn-Hilliard Equation
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Well-posedness of 2-D hyperbolic viscous Cahn-Hilliard equation
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Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation
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Uniform Cooling of Alloys
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Postprocessing Mixed Finite Element Methods For Solving Cahn–Hilliard Equation: Methods and Error Analysis
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A Robust Solver for a Mixed Finite Element Method for the Cahn–Hilliard Equation
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Recovery Type a Posteriori Error Estimation of an Adaptive Finite Element Method for Cahn–Hilliard Equation
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A Higher Order Nonconforming Virtual Element Method for the Cahn–Hilliard Equation
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The Convergence Analysis of a Class of Stabilized Semi-Implicit Isogeometric Methods for the Cahn-Hilliard Equation
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Optimal Error Estimates of Energy-Stable Runge–Kutta Methods for the $$\varepsilon $$-dependent Cahn-Hilliard/Allen-Cahn Equation
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Upper Bounds for Coarsening for the Deep Quench Obstacle Problem
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Optimal distributed control of nonlinear Cahn–Hilliard systems with computational realization
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Studying the interphase zone in a certain singular-limit problem
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Well-posedness for Cahn–Hilliard-type model on the half-line
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On the choice of auxiliary linear operator in the optimal homotopy analysis of the Cahn-Hilliard initial value problem
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B-method approach to blow-up solutions of fourth-order semilinear parabolic equations
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Remarks on Sharp Interface Limit for an Incompressible Navier-Stokes and Allen-Cahn Coupled System
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A three level linearized compact difference scheme for the Cahn-Hilliard equation
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Weak Solutions to the Anisotropic Degenerate Cahn–Hilliard Equation with Logarithmic Potential
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A discretization method for nonlocal diffusion type equations
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Numerical Methods for Solving the Cahn–Hilliard Equation and Its Applicability to Related Energy-Based Models
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Toward Predictive Multiscale Modeling of Vascular Tumor Growth
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Global Existence and Lp Decay Estimate of Solutions for Viscous Cahn-Hilliard Equation with Inertial Term
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Time-periodic solution of a 2D fourth-order nonlinear parabolic equation
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The regularity of the solutions for a stochastic 2D Cahn-Hilliard-Oldroyd model of order one
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General Solution for the Second-Order Nonlocal Linear Differential Equation
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Higher order spectral element scheme for two- and three-dimensional Cahn–Hilliard equation
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Analysis of multilevel finite volume approximation of 2D convective Cahn–Hilliard equation
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On the Global Attractor of Modified Swift-Hohenberg Equation in 3D Case
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The existence of weak solutions for a nonlocal Cahn-Hilliard equation with degenerate mobility
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Nonlinear Galerkin finite element methods for fourth-order Bi-flux diffusion model with nonlinear reaction term
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The existence of Non-blow-up phenomenon for a generalized nonlocal Cahn–Hilliard equation with degenerate mobility
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Fourier Spectral Approximation to Global Attractor for 2D Convective Cahn–Hilliard Equation
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Strong Solutions to the Density-Dependent Incompressible Nematic Liquid Crystal Flows with Heat Effect
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The regularity of the solutions for a stochastic 2D Allen–Cahn–Navier–Stokes model
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On the longtime behavior of a viscous Cahn–Hilliard system with convection and dynamic boundary conditions
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Long-time behavior of the Cahn–Hilliard equation with dynamic boundary condition
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A Large Time-Stepping Mixed Finite Method of the Modified Cahn–Hilliard Equation
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Slow motion for the Cahn-Hilliard equation in one space dimension
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On the existence of nonnegative continuous solutions of the Cahn-Hilliard equation
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Spectral comparison principles for the Cahn-Hilliard and phase-field equations, and time scales for coarsening
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A mathematical model of dynamics of non-isothermal phase separation
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Numerical computations of coarsening in the one-dimensional Cahn-Hilliard model of phase separation
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Singularities in a modified Kuramoto-Sivashinsky equation describing interface motion for phase transition
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Feedback stabilization and optimal control for the Cahn-Hilliard equation
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A numerical method for the nonlinear Cahn-Hilliard equation with nonperiodic boundary conditions
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Phase changes in a thin plate with non-local self-stress effects
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The phase field method for geometric moving interfaces and their numerical approximations
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Optimal control of geometric partial differential equations
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The Fourier spectral method for the Cahn–Hilliard equation
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The Cahn–Hilliard type equations with periodic potentials and sources
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A thin film equation with a singular diffusion
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A virtual element method for the Cahn–Hilliard problem in mixed form
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The least squares spectral element method for the Cahn–Hilliard equation
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Enhanced dissipation by advection and applications to PDEs
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A conservative difference scheme for the viscous Cahn–Hilliard equation with a nonconstant gradient energy coefficient
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Finite element approximations for a linear fourth-order parabolic SPDE in two and three space dimensions with additive space–time white noise
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Long time Hαs stability of a classical scheme for Cahn-Hilliard equation with polynomial nonlinearity
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Solving phase-field models in the tensor train format to generate microstructures of bicontinuous composites
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Dissipation-preserving discretization of the Cahn–Hilliard equation with dynamic boundary conditions
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Analysis of a line method for reaction-diffusion models of nonlocal type
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Error estimates of time discretizations for a Cahn-Hilliard phase-field model for the two-phase magnetohydrodynamic flows
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Error estimate for the Cahn-Hilliard equation by the SAV-Runge-Kutta scheme
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A local discontinuous Galerkin method for the cubic-quintic complex Ginzburg-Landau equation: Vortex solitons and collision dynamics
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Computational Investigation of Ripple Dynamics in Biofilms in Flowing Systems
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Energy method for structure-preserving finite difference schemes and some properties of difference quotient
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An energy stable fourth order finite difference scheme for the Cahn–Hilliard equation
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Stabilized semi-implicit numerical schemes for the Cahn–Hilliard-like equation with variable interfacial parameter
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Direct solver for the Cahn–Hilliard equation by Legendre–Galerkin spectral method
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A robust solver for a second order mixed finite element method for the Cahn–Hilliard equation
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Unconditionally energy stable discontinuous Galerkin schemes for the Cahn–Hilliard equation
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A high order numerical scheme for a nonlinear nonlocal reaction–diffusion model arising in population theory
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Optimal error estimates for a decoupled, fully discrete scheme for the 2D/3D diffuse interface two-phase MHD flows
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Second order schemes and time-step adaptivity for Allen–Cahn and Cahn–Hilliard models
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Energy-stable linear schemes for polymer–solvent phase field models
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An L∞ bound for solutions of a fractional Cahn–Hilliard equation
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The robust physics-informed neural networks for a typical fourth-order phase field model
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Simulation of the phase field Cahn–Hilliard and tumor growth models via a numerical scheme: Element-free Galerkin method
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A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamic flows
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On the approximate solution to an initial boundary valued problem for the Cahn–Hilliard equation
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Numerical analysis of energy stable weak Galerkin schemes for the Cahn–Hilliard equation
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Convergence of substructuring methods for the Cahn–Hilliard equation
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On the convergence of linear and nonlinear Parareal methods for the Cahn–Hilliard equation
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Invariant sample measures and sample statistical solutions for nonautonomous stochastic lattice Cahn–Hilliard equation with nonlinear noise
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Physical, mathematical, and numerical derivations of the Cahn–Hilliard equation
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Simulation of lower bainitic transformation with the phase-field method considering carbide formation
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IMEX methods for thin-film equations and Cahn–Hilliard equations with variable mobility
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Multifidelity methods for uncertainty quantification of a nonlocal model for phase changes in materials
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cuPentBatch—A batched pentadiagonal solver for NVIDIA GPUs
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Pore-scale modeling of multiple fluids flow transport kinetics for CO2 enhanced gas recovery
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A numerical method based on the boundary integral equation and dual reciprocity methods for one-dimensional Cahn–Hilliard equation
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The numerical solution of Cahn–Hilliard (CH) equation in one, two and three-dimensions via globally radial basis functions (GRBFs) and RBFs-differential quadrature (RBFs-DQ) methods
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Pore-scale simulation of multi-fluid flow transport dynamics for hydrogen geological storage in depleted gas reservoirs
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A discontinuous Galerkin method for the Cahn–Hilliard equation
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A nonconforming finite element method for the Cahn–Hilliard equation
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On linear schemes for a Cahn–Hilliard diffuse interface model
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A quantitative comparison between and elements for solving the Cahn–Hilliard equation
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Isogeometric analysis of the advective Cahn–Hilliard equation: Spinodal decomposition under shear flow
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Computational investigation of porous media phase field formulations: Microscopic, effective macroscopic, and Langevin equations
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