Periodic solutions for the Allen-Cahn equation
نویسندگان
چکیده
منابع مشابه
Superabundance of Stationary Solutions for the Discrete Allen-cahn Equation
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 sol...
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has been studied for several decades and is an important nonlinear PDE due to the fact that it lies at the interface of several different mathematical fields. The famous De Giorgi conjecture states that any entire solution to (1) in R which is monotone in one direction should be one dimensional, at least for n ≤ 8. The conjecture was proved in dimension n = 2 by Ghoussoub-Gui ([13]) and dimensi...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2015
ISSN: 1687-1847
DOI: 10.1186/s13662-015-0631-3