Superabundance of Stationary Solutions for the Discrete Allen-cahn Equation
نویسنده
چکیده
The discrete Allen-Cahn equation is a spatially discrete analogue of the Allen-Cahn equation, a parabolic partial differential equation proposed as a simple model for phase separation in materials. In some sense, the solutions of the discrete equation display a richer variety of behaviors than do the corresponding solutions of the continuous equation. In particular, the number of stationary solutions of the two equations may not agree, even when the lattice of the discrete equation is extremely fine. We will discuss this phenomenon, as well as its implications in areas such as dynamical metastability. AMS(MOS) subject classification: 58F21, 34C35
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تاریخ انتشار 1998