Recent Submissions

  • Stability of Curved Interfaces in the Perturbed Two-Dimensional Allen-Cahn System 

    Iron, David, Theodore Kolokolonikov, John Rumsey, and Juncheng Wei. 2009. "Stability of Curved Interfaces in the Perturbed Two-Dimensional Allen-Cahn System." SIAM Journal on Applied Mathematics 69(5): 1228-16.
    We consider the singular limit of a perturbed Allen-Cahn model on a bounded two-dimensional domain: $\left\{\begin{array}{@{}ll@{}} u_t = \varepsilon^2 \Delta u - 2 (u - \varepsilon a) (u^2 - 1), & x \in \Omega \subset ...