Stationary Solutions of Driven Fourth- and Sixth-Order Cahn--Hilliard-Type Equations

@article{Korzec2008StationarySO,
  title={Stationary Solutions of Driven Fourth- and Sixth-Order Cahn--Hilliard-Type Equations},
  author={Maciek D. Korzec and P. L. Evans and Andreas M{\"u}nch and Barbara Wagner},
  journal={SIAM Journal of Applied Mathematics},
  year={2008},
  volume={69},
  pages={348-374}
}
New types of stationary solutions of a one-dimensional driven sixth-order Cahn–Hilliard-type equation that arises as a model for epitaxially growing nanostructures, such as quantum dots, are derived by an extension of the method of matched asymptotic expansions that retains exponentially small terms. This method yields analytical expressions for far-field behavior as well as the widths of the humps of these spatially nonmonotone solutions in the limit of small driving force strength, which is… CONTINUE READING

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