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Ginzburg-Landau equation and motion by mean curvature, I: Convergence
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
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On the slowness of phase boundary motion in one space dimension
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Phase transitions and generalized motion by mean curvature
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Generalized Motion by Curvature with a Dirichlet Condition
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Anisotropic Motion of an Interface Relaxed by the Formation of Infinitesimal Wrinkles
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The Motion of Multiple-Phase Junctions under Prescribed Phase-Boundary Velocities
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Controlled Markov Processes and Viscosity Solutions
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Surface tension and supercooling in solidification theory
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Curvature Dependent Phase Boundary Motion and Parabolic Double Obstacle Problems
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Phase Field Equations in the Singular Limit of Sharp Interface Problems
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Solutions for the Two-Phase Stefan Problem with the Gibbs—Thomson Law for the Melting Temperature
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The gradient theory of phase transitions and the minimal interface criterion
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The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
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A remark on regularization in Hilbert spaces
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Motion of level sets by mean curvature III
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Ginzburg-Landau equation and motion by mean curvature, II: Development of the initial interface
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Generalized motion by mean curvature with Neumann conditions and the Allen-Cahn model for phase transitions
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Motion of level sets by mean curvature IV
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A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening
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Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
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Crystal growth and dendritic solidification
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Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics
inferredcites →https://doi.org/10.1016/0022-0396(91)90163-4openalex-snapshot
Slow motion for the Cahn-Hilliard equation in one space dimension
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Generation and propagation of interfaces for reaction-diffusion equations
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Thermodynamically consistent models of phase-field type for the kinetic of phase transitions
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Continuum theory of thermally induced phase transitions based on an order parameter
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Efficient computation of a sharp interface by spreading via phase field methods
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Overview No. 98 I—Geometric models of crystal growth
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The gradient theory of phase transitions for systems with two potential wells
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Development of interfaces in ℝ N
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Solutions for the two-phase Stefan problem with the Gibbs–Thomson Law for the melting temperature
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Discontinuous solutions of deterministic optimal stopping time problems
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Two-Dimensional Motion of Idealized Grain Boundaries
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Spectrum for the allen-chan, chan-hillard, and phase-field equations for generic interfaces
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Elliptic regularization and partial regularity for motion by mean curvature
inferredcites →https://doi.org/10.1090/s0002-9939-1987-0884461-3openalex-snapshot
A Simple, Direct Proof of Uniqueness for Solutions of the Hamilton-Jacobi Equations of Eikonal Type
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Viscosity solutions of Hamilton-Jacobi equations
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Some properties of viscosity solutions of Hamilton-Jacobi equations
inferredcites →https://doi.org/10.1090/s0002-9947-1992-1068927-8openalex-snapshot
Motion of Level Sets by Mean Curvature. II
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Geometrical evolution of developed interfaces
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User’s guide to viscosity solutions of second order partial differential equations
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Nonlocal reaction—diffusion equations and nucleation
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Thermomechanics of Evolving Phase Boundaries in the Plane
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Front migration in the nonlinear Cahn-Hilliard equation
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Minimizers and gradient flows for singularly perturbed bi-stable potentials with a Dirichlet condition
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Asymptotics for a parabolic double obstacle problem
inferredcites →https://doi.org/10.1103/physreva.39.5887openalex-snapshot
Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations
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Diffuse interface model of diffusion-limited crystal growth
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Universal Scaling in the Motion of Random Interfaces
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Dynamics of Layered Interfaces Arising from Phase Boundaries
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Fast Reaction, Slow Diffusion, and Curve Shortening
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Reaction-Diffusion Processes and Evolution to Harmonic Maps
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Curvature-Driven Flows: A Variational Approach
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Front Propagation and Phase Field Theory
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A Simple Proof of Convergence for an Approximation Scheme for Computing Motions by Mean Curvature
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Dynamics of Internal Layers and Diffusive Interfaces
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Phase field methods for free boundary problems
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A short note on the evolution of a surface by its mean curvature
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Parabolic Equations for Curves on Surfaces Part I. Curves with p-Integrable Curvature
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Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
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Viscosity Solutions of Hamilton-Jacobi Equations
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Parabolic Equations for Curves on Surfaces: Part II. Intersections, Blow-up and Generalized Solutions
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Motion of hypersurfaces and geometric equations
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Generalized interface evolution with the Neumann boundary condition
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Asymptotic behavior for singularities of the mean curvature flow
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Motion of level sets by mean curvature. I
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Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
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Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
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Flat flow is motion by crystalline curvature for curves with crystalline energies
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What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Phase transition of parabolic Ginzburg–Landau equation with potentials of high‐dimensional wells
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Scaling Limits for Pinned Gaussian Random Interfaces in the Presence of Two Possible Candidates
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