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Second order asymptotics for the propagation speed of interfaces in the Allen‐Cahn phase field model for elastic solids
Author(s) -
Alber HansDieter,
Markert Bernd
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210009
Subject(s) - allen–cahn equation , elasticity (physics) , asymptotic expansion , phase (matter) , field (mathematics) , order (exchange) , mathematical analysis , physics , mathematics , mathematical physics , thermodynamics , quantum mechanics , pure mathematics , finance , economics
For a phase field model, which consists of the elasticity equations coupled to the Allen‐Cahn equation, we state an asymptotic expansion for the propagation speed of the diffusive interface. The error of the expansion is of order η 2 , where η is the width of the interface. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)