On the Stationary Cahn--Hilliard Equation: Bubble Solutions
Juncheng Wei, Matthias Winter · SIAM Journal on Mathematical Analysis · 1998
We study stationary solutions of the Cahn--Hilliard equation in a bounded smooth domain that have an interior spherical interface (bubbles). We show that a large class of interior points (the "nondegenerate peak" points) have the following property: there exists such a solution whose bubble center lies close to a given nondegenerate peak point. Our construction uses, among others, the Liapunov--Schmidt reduction method and exponential asymptotics.