Second order asymptotics for the propagation speed of interfaces in the Allen-Cahn phase field model for elastic solids



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 η2, where η is the width of the interface. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)