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Applied Math Seminar – Toai Luong (University of Alabama)
February 7 @ 11:00 am - 12:00 pm
Title: Minimizers for the Cahn-Hilliard energy functional under the Dirichlet boundary conditions
Abstract: We study the minimizers for the Cahn-Hilliard energy functional with a symmetric quartic double-well potential and under the Dirichlet boundary conditions. Using the Nehari manifold method and connecting it to the eigenvalue problem for the negative Laplacian with the homogeneous boundary condition, we prove that if the boundary value is exactly the average of the two pure phases, depending on the relation between the bifurcation parameter and the smallest eigenvalue, there can be a unique minimizer or there can be exactly two minimizers. If the boundary value is in between one pure phase and the average of the two pure phases, then the minimizer is unique and is also within the same range.