Existence and Classification of Solutions to the Cahn-Hilliard Equation


Tuesday, July 12th 11:30-12:00, 2019
Logistar Room at DeustoTech, University of Deusto.

Matteo Rizzi
Centro de Modelamiento Matemático, Universidad de Chile, Santiago, Chile.

In the talk I will present the construction of a family {uε} of solutions to the Cahn-Hilliard equation $-\varepsilon \Delta u_{\varepsilon}=\varepsilon^{-1}\left(u_{\varepsilon}-u_{\varepsilon}^{3}\right)-\ell_{\varepsilon}, \quad \ell_{\varepsilon} \in \mathbb{R}$ whose zero level set is prescribed and approaches, as ε → 0, a given complete, embedded, k-ended constant mean curvature surface. It is a joint work with Michal Kowalczyk. Moreover, I will present some classication results, dealing with properties such as boundedness, monotonicity and radial symmetry.