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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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Asymptotic stability analysis for transition front solutions in Cahn-Hilliard systems

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Title
Asymptotic stability analysis for transition front solutions in Cahn-Hilliard systems
Author
Howard, PeterKwon, Bongsuk
Keywords
Asymptotic behaviors; Cahn-Hilliard systems; Eigen-value; Essential spectrum; Evans function; Linearized operators; Non-linear stabilities; Semi-group; Shift invariance; Transition fronts
Issue Date
201207
Publisher
ELSEVIER SCIENCE BV
Citation
PHYSICA D-NONLINEAR PHENOMENA, v.241, no.14, pp.1193 - 1222
Abstract
We consider the asymptotic behavior of perturbations of transition front solutions arising in Cahn-Hilliard systems on R. Such equations arise naturally in the study of phase separation, and systems describe. cases in which three or more phases are possible. When a Cahn-Hilliard system is linearized about a transition front solution, the linearized operator has an eigenvalue at 0 (due to shift invariance), which is not separated from essential spectrum. In cases such as this, nonlinear stability cannot be concluded from classical semigroup considerations and a more refined development is appropriate. Our main result asserts that spectral stability - a necessary condition for stability, defined in terms of an appropriate Evans function - implies nonlinear stability.
URI
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DOI
http://dx.doi.org/10.1016/j.physd.2012.04.002
ISSN
0167-2789
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