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Rotationally symmetric solutions to the Cahn-Hilliard equation

  • Author Bio: E-mail address: ahernandez@dim.uchile.cl; E-mail address: kowalczy@dim.uchile.cl
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  • This paper is devoted to construction of new solutions to the Cahn-Hilliard equation in $\mathbb R^d$. Staring from the Delaunay unduloid $D_τ$ with parameter $τ∈ (0,τ^*)$ we find for each sufficiently small $\varepsilon $ a solution $u$ of this equation which is periodic in the direction of the $x_d$ axis and rotationally symmetric with respect to rotations about this axis. The zero level set of $u$ approaches as $\varepsilon \to 0$ the surface $D_τ$ . We use a refined version of the Lyapunov-Schmidt reduction method which simplifies very technical aspects of previous constructions for similar problems.

    Mathematics Subject Classification: Primary:35J61, 35B08, 35B07, 35B10, 35B36; Secondary: 35Q56, 35Q79.


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