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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 L-p stability for transition fronts in Cahn-Hilliard systems

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Title
Asymptotic L-p stability for transition fronts in Cahn-Hilliard systems
Author
Howard, PeterKwon, Bongsuk
Keywords
Cahn-Hilliard systems; Evans function; Spinodal decomposition; Stability; Transition fronts
Issue Date
201205
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation
JOURNAL OF DIFFERENTIAL EQUATIONS, v.252, no.10, pp.5814 - 5831
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 processes, 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 if initial perturbations are small in L-1 boolean AND L-infinity then spectral stability-a necessary condition for stability, defined in terms of an appropriate Evans function implies asymptotic nonlinear stability in LP for all 1
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DOI
http://dx.doi.org/10.1016/j.jde.2012.01.033
ISSN
0022-0396
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