Pattern-forming fronts in a Swift-Hohenberg equation with directional quenching - parallel and oblique stripes
arXiv:1708.03815 · doi:10.1112/jlms.12122
Abstract
We study the effect of domain growth on the orientation of striped phases in a Swift-Hohenberg equation. Domain growth is encoded in a step-like parameter dependence that allows stripe formation in a half plane, and suppresses patterns in the complement, while the boundary of the pattern-forming region is propagating with fixed normal velocity. We construct front solutions that leave behind stripes in the pattern-forming region that are parallel to or at a small oblique angle to the boundary. Technically, the construction of stripe formation parallel to the boundary relies on ill-posed, infinite-dimensional spatial dynamics. Stripes forming at a small oblique angle are constructed using a functional-analytic, perturbative approach. Here, the main difficulties are the presence of continuous spectrum and the fact that small oblique angles appear as a singular perturbation in a traveling-wave problem. We resolve the former difficulty using a farfield-core decomposition and Fredholm theory in weighted spaces. The singular perturbation problem is resolved using preconditioners and boot-strapping.
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Cited by in corpus (5)
- Phase separation patterns from directional quenching
- Spectral stability of pattern-forming fronts in the complex Ginzburg-Landau equation with a quenching mechanism
- Contact angle selection for interfaces in growing domains
- Reflections in excitable media linked to existence and stability of one-dimensional spiral waves
- Strain and defects in oblique stripe growth