In this paper we prove an asymptotic estimate, up to the second-order included, on the behaviour of the onedimensional Allen-Cahn's action functionals, around a periodic function with bounded variation and taking values in ±1. The leading term of this estimate justifies and confirms, from a variational point of view, the results of Fusco-Hale [Dyn. Diff. Equation 1 (1989), 75-94] and Carr-Pego [Comm. Pure Appl. Math. 42 (1989), 523-576] on the exponentially slow motion of metastable patterns coexisting at the transition temperature.
Bellettini, G., Nayam A., H., Novaga, M. (2015). Gamma-type estimates for the one-dimensional Allen-Cahn's action. ASYMPTOTIC ANALYSIS, 94(1-2), 161-185 [10.3233/ASY-151308].
Gamma-type estimates for the one-dimensional Allen-Cahn's action
Bellettini, Giovanni;
2015-01-01
Abstract
In this paper we prove an asymptotic estimate, up to the second-order included, on the behaviour of the onedimensional Allen-Cahn's action functionals, around a periodic function with bounded variation and taking values in ±1. The leading term of this estimate justifies and confirms, from a variational point of view, the results of Fusco-Hale [Dyn. Diff. Equation 1 (1989), 75-94] and Carr-Pego [Comm. Pure Appl. Math. 42 (1989), 523-576] on the exponentially slow motion of metastable patterns coexisting at the transition temperature.
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https://hdl.handle.net/11365/1017468