Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.physd.2010.05.008
Title: Stability of travelling wave solutions for coupled surface and grain boundary motion
Authors: Beck, M.
Pan, Z. 
Wetton, B.
Keywords: Free boundary
Grain boundary
Linear stability
Mean curvature motion
Spectrum
Surface diffusion
Issue Date: 1-Sep-2010
Source: Beck, M., Pan, Z., Wetton, B. (2010-09-01). Stability of travelling wave solutions for coupled surface and grain boundary motion. Physica D: Nonlinear Phenomena 239 (17) : 1730-1740. ScholarBank@NUS Repository. https://doi.org/10.1016/j.physd.2010.05.008
Abstract: We investigate the spectral stability of the travelling wave solution for the coupled motion of a free surface and grain boundary that arises in materials science. In this problem a grain boundary, which separates two materials that are identical except for their crystalline orientation, evolves according to mean curvature. At a triple junction, this boundary meets the free surfaces of the two crystals, which move according to surface diffusion. The model is known to possess a unique travelling wave solution. We study the linearization about the wave, which necessarily includes a free boundary at the location of the triple junction. This makes the analysis more complex than that of standard travelling waves, and we discuss how existing theory applies in this context. Furthermore, we compute numerically the associated point spectrum by restricting the problem to a finite computational domain with appropriate physical boundary conditions. Numerical results strongly suggest that the two-dimensional wave is stable with respect to both two- and three-dimensional perturbations. © 2010 Elsevier B.V. All rights reserved.
Source Title: Physica D: Nonlinear Phenomena
URI: http://scholarbank.nus.edu.sg/handle/10635/126646
ISSN: 01672789
DOI: 10.1016/j.physd.2010.05.008
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