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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