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Hyperbolic non-conserved phase field equations

Authors
Journal
Journal of Crystal Growth
0022-0248
Publisher
Elsevier
Publication Date
Identifiers
DOI: 10.1016/s0022-0248(98)01008-2
Keywords
  • Phase Transitions
  • Phase Field Equations
  • Born–Infield Equation
  • Memory Effects

Abstract

Abstract We consider the following hyperbolic system of PDEs which generalize the classical phase field equations with a non-conserved order parameter φ and temperature u: u tt+ε 2φ tt+γ 1u t+ε 2γ 1φ t=α Δu, ε 2φ tt+γ 2ε 2φ t=ε 2 Δφ+f(φ)+εu for ε≪1. We present the model, derive a law for the evolution of the interface which generalizes the classical flow by mean curvature equation, and analyze the evolution of some simply shaped interfaces.

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