Business Faculty Research, Publications and Presentations
http://hdl.handle.net/10222/36351
2022-09-30T22:01:20ZStability of Curved Interfaces in the Perturbed Two-Dimensional Allen-Cahn System
http://hdl.handle.net/10222/37345
Stability of Curved Interfaces in the Perturbed Two-Dimensional Allen-Cahn System
Iron, David; Kolokolonikov, Theodore; Rumsey, John; Wei, Juncheng
We consider the singular limit of a perturbed Allen-Cahn model on a bounded two-dimensional domain: $\left\{\begin{array}{@{}ll@{}} u_t = \varepsilon^2 \Delta u - 2 (u - \varepsilon a) (u^2 - 1), & x \in \Omega \subset \mathbb{R}^2 \ \partial_n u = 0, & x \in \partial \Omega \end{array} \right.$ where $\varepsilon$ is a small parameter and $a$ is an $O(1)$ quantity. We study equilibrium solutions that have the form of a curved interface. Using singular perturbation techniques, we fully characterize the stability of such an equilibrium in terms of a certain geometric eigenvalue problem, and give a simple geometric interpretation of our stability results. Full numerical computations of the time-dependent PDE as well as of the associated two-dimensional eigenvalue problem are shown to be in excellent agreement with the analytical predictions.
2009-01-01T00:00:00ZYonggan Zhao CV
http://hdl.handle.net/10222/37018
Yonggan Zhao CV
Zhao, Yonggan
2013-09-30T00:00:00ZIssues of the ends of life
http://hdl.handle.net/10222/36312
Issues of the ends of life
Waite, Terry; Downie, Jocelyn; Lebacqz, Karen; Chochinov, Harvey M.; Thompson, Genevieve; Blakeney, Allan E.; Beresford, Eric; Christie, Innis; Stuewe, David
Buley, David
2013-01-01T00:00:00Z