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, Peter; Kwon, Bongsuk
- Issue Date
- 2012-05
- 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
- URI
- https://scholarworks.unist.ac.kr/handle/201301/2991
- URL
- http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84858277258
- DOI
- 10.1016/j.jde.2012.01.033
- ISSN
- 0022-0396
- Appears in Collections:
- MTH_Journal Papers
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