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Kwon, Bongsuk
Partial Differential Equations and their applications
Research Interests
  • Partial differential equations, hyperbolic conservation laws, stability of nonlinear waves

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SPECTRAL ANALYSIS FOR TRANSITION FRONT SOLUTIONS IN CAHN-HILLIARD SYSTEMS

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Title
SPECTRAL ANALYSIS FOR TRANSITION FRONT SOLUTIONS IN CAHN-HILLIARD SYSTEMS
Author
Howard, PeterKwon, Bongsuk
Issue Date
2012-01
Publisher
AMER INST MATHEMATICAL SCIENCES
Citation
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.32, no.1, pp.125 - 166
Abstract
We consider the spectrum associated with the linear operator ob- tained when a Cahn{Hilliard system on ℝ is linearized about a transition wave solution. In many cases it's possible to show that the only non-negative ei- genvalue is λ = 0, and so stability depends entirely on the nature of this neutral eigenvalue. In such cases, we identify a stability condition based on an appropriate Evans function, and we verify this condition under strong struc- tural conditions on our equations. More generally, we discuss and implement a straightforward numerical check of our condition, valid under mild structural conditions
URI
https://scholarworks.unist.ac.kr/handle/201301/9902
URL
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84858289647
DOI
10.3934/dcds.2012.32.125
ISSN
1078-0947
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