Metastable Dynamics and Spatially Inhomogeneous Equilibria in Dumbell-shaped Domains
نویسنده
چکیده
The motion of internal layers for three singularly perturbed reaction diiusion problems, including the Allen-Cahn equation, is studied in a two-dimensional dumbell-shaped domain. The channel region that connects the two attachments, or lobes, of the dumbell is taken to be rectangular. The motion of straight-line internal layers in the channel region is analyzed using an asymptotic projection method. This motion is shown to be metastable and highly dependent on the local convexity properties of the boundary near the contact region between the ends of the channel and the two attachments. When the domain is non-convex it is shown that the metastable internal layers dynamics in the channel tends, as t ! 1, to a limiting stable spatially inhomogeneous equilibrium solution.
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تاریخ انتشار 1999