NDLI: The Stability and Evolution of Curved Domains Arising from One-Dimensional Localized Patterns

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Lindsay, Alan E. Glasner, Karl B.
Copyright Year	2013
Abstract	In many pattern forming systems, narrow two-dimensional domains can arise whose cross sections are roughly one-dimensional localized solutions. This paper investigates this phenomenon in the variational Swift--Hohenberg equation. Stability of straight line solutions is analyzed, leading to criteria for either curve buckling or curve disintegration. Matched asymptotic expansions are used to derive a two-term expression for the geometric motion of curved domains, which includes both elastic and surface diffusion-type regularizations of curve motion. This leads to novel equilibrium curves and space-filling pattern proliferation. Numerical tests are used to confirm and illustrate these phenomena.
Starting Page	650
Ending Page	673
Page Count	24
File Format	PDF
DOI	10.1137/120893008
e-ISSN	15360040
Issue Number	2
Volume Number	12
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2013-05-02
Access Restriction	Subscribed
Subject Keyword	Pattern formation Stability geometric motion localized states surface diffusion matched asymptotics Singular perturbations Higher-order parabolic equations curvature
Content Type	Text
Resource Type	Article

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