Interface conditions for a phase field model with anisotropic and non-local interactions

DOI10.1007/s00205-011-0429-8zbMath1256.35209OpenAlexW2000057597MaRDI QIDQ715334

Emre Esenturk, Xinfu Chen, Gunduz Caginalp

Publication date: 5 November 2012

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-011-0429-8

Mathematics Subject Classification ID

Dynamics of phase boundaries in solids (74N20) Stefan problems, phase changes, etc. (80A22) Free boundary problems for PDEs (35R35) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Related Items (10)

Higher-order anisotropic Caginalp phase-field systems ⋮ Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations ⋮ Higher-order anisotropic models in phase separation ⋮ A phase field approach for direct calculation of interfacial free energy of solid-gas and solid-liquid interfaces in Lennard-Jones systems ⋮ Asymptotic behavior of spreading fronts in the anisotropic Allen-Cahn equation on \(\mathbb{R}^n\) ⋮ ON HIGHER-ORDER ANISOTROPIC CAGINALP PHASE-FIELD SYSTEMS WITH POLYNOMIAL NONLINEAR TERMS ⋮ On higher-order anisotropic conservative Caginalp phase-field systems ⋮ Time discretization of a nonlinear phase field system in general domains ⋮ On higher-order anisotropic conservative Caginalp phase-field type models ⋮ The Cahn-Hilliard equation and some of its variants

Cites Work

• Unnamed Item
• Anisotropic phase field equations of arbitrary order
• Motion of level sets by mean curvature. I
• A rapidly converging phase field model
• A generalization of the Caginalp phase-field system based on the Cattaneo law
• The role of microscopic anisotropy in the macroscopic behavior of a phase boundary
• Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations
• Traveling wave solutions for a nonlocal phase-field system
• A Stefan problem with surface tension as the sharp interface limit of a nonlocal system of phase-field type
• On a nonlocal phase-field system
• Phase transitions and generalized motion by mean curvature
• Convergence of the phase field model to its sharp interface limits
• Geometrical Evolution of Developed Interfaces
• Non-local temperature-dependent phase-field models for non-isothermal phase transitions
• Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations

This page was built for publication: Interface conditions for a phase field model with anisotropic and non-local interactions