Stability of travelling wave solutions for coupled surface and grain boundary motion
type: Item
instance of: scholarly article
title: Stability of travelling wave solutions for coupled surface and grain boundary motion
zbMATH Open document ID: 1209.37093
author: Yanyan Li
published in: Physica D
publication date: 2010-09-24T00:00:00Z
review text: The authors 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. They 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. Furthermore, they 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.
reviewed by: Norbert Koksch
Mathematics Subject Classification ID: 37L15
Mathematics Subject Classification ID: 35Q60
zbMATH DE Number: 5791162
zbMATH Keywords: grain boundary
zbMATH Keywords: mean curvature motion
zbMATH Keywords: surface diffusion
zbMATH Keywords: linear stability
zbMATH Keywords: spectrum
zbMATH Keywords: free boundary
zbMATH Keywords: travelling wave
MaRDI profile type: Publication
full work available at URL: j.physd.2010.05.008
OpenAlex ID: W2090013860
cites work: On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation
cites work: A singular limit for a system of degenerate Cahn-Hilliard equations
cites work: On the Variational Approximation of Combined Second and Fourth Order Geometric Evolution Equations
cites work: A numerical method for coupled surface and grain boundary motion
cites work: Towards a Statistical Theory of Texture Evolution in Polycrystals
cites work: Coupled surface and grain boundary motion: a travelling wave solution
cites work: Coupled surface and grain boundary motion: nonclassical traveling-wave solutions
cites work: A parametric finite element method for fourth order geometric evolution equations
cites work: A general approach to stability in free boundary problems
cites work: Stability of travelling waves with interface conditions
cites work: Stability of traveling waves: dichotomies and eigenvalue conditions on finite intervals
cites work: Q4550350
cites work: Absolute and convective instabilities of waves on unbounded and large bounded domains
cites work: Defects in Oscillatory Media: Toward a Classification
DOI: 10.1016/J.PHYSD.2010.05.008
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description: scientific article; zbMATH DE number 5791162