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• W2771311209 abstract "In this paper we construct entire solutions to the Cahn-Hilliard equation $-Delta(-Delta u+W^{'}(u))+W^{}(u)(-Delta u+W^{'}(u))=0$ in the Euclidean plane, where $W(u)$ is the standard double-well potential $frac{1}{4} (1-u^2)^2$. Such solutions have a non-trivial profile that shadows a Willmore planar curve, and converge uniformly to $pm 1$ as $x_2 to pm infty$. These solutions give a counterexample to the counterpart of Gibbons' conjecture for the fourth-order counterpart of the Allen-Cahn equation. We also study the $x_2$-derivative of these solutions using the special structure of Willmore's equation." @default.
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• W2771311209 date "2017-12-04" @default.
• W2771311209 modified "2023-09-30" @default.
• W2771311209 title "Periodic Solutions to a Cahn–Hilliard–Willmore Equation in the Plane" @default.
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• W2771311209 doi "https://doi.org/10.1007/s00205-017-1206-0" @default.
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