Asymptotic Lp stability for transition fronts in Cahn–Hilliard systems Academic Article uri icon

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∩L ∞ then spectral stability-a necessary condition for stability, defined in terms of an appropriate Evans function-implies asymptotic nonlinear stability in L p for all 1

author list (cited authors)

  • Howard, P., & Kwon, B.

citation count

  • 5

publication date

  • May 2012