A sharp interface limit of the phase field equations: one-dimensional and axisymmetric

DOI10.1017/S0956792500002606zbMath0876.35133MaRDI QIDQ4340595

Barbara E. E. Stoth

Publication date: 7 July 1997

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

energy estimatesradial symmetryphase-field equationsStefan problem with surface tension

Mathematics Subject Classification ID

Stefan problems, phase changes, etc. (80A22) Free boundary problems for PDEs (35R35)

Related Items (5)

A phase-field theory for solidification based on a general anisotropic sharp-interface theory with interfacial energy and entropy ⋮ Spectrum for the allen-chan, chan-hillard, and phase-field equations for generic interfaces ⋮ On anisotropic order parameter models for multi-phase systems and their sharp interface limits ⋮ Analysis of a fully discrete finite element method for the phase field model and approximation of its sharp interface limits ⋮ The quasistationary phase field equations with Neumann boundary conditions

Cites Work

• Thermodynamically consistent models of phase-field type for the kinetics of phase transitions
• An analysis of a phase field model of a free boundary
• Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics
• On the slowness of phase boundary motion in one space dimension
• Global Existence of Weak Solutions for Interface Equations Coupled with Diffusion Equations
• Phase transitions and generalized motion by mean curvature
• Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations
• Metastable patterns in solutions of u_t = ϵ²u_xx − f(u)

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