When describing the anisotropic evolution of microstructures in solids using phase-field models, the anisotropy of the crystalline phases is usually introduced into the interfacial energy by directional dependencies of the gradient energy coefficients. We consider an alternative approach based on a wavelet analogue of the Laplace operator that is intrinsically anisotropic and linear. The paper focuses on the classical coupled temperature/Ginzburg--Landau type phase-field model for dendritic growth. For the model based on the wavelet analogue, existence, uniqueness and continuous dependence on initial data are proved for weak solutions. Numerical studies of the wavelet based phase-field model show dendritic growth similar to the results obtained for classical phase-field models.
|Number of pages
|Discrete and Continuous Dynamical Systems - Series B
|Published - Apr 1 2016
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: The first author acknowledges the support by the DFG Matheon research centre, within the project C10, SENBWF in the framework of the program Spitzenforschung und Innovation in den Neuen Landern, Grant Number 03IS2151 and KAUST, award No. KUK-C1-013-04, and the hospitality of the Mathematical Institute at the University of Oxford during his Visiting Postdoctoral Fellowship.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.