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Metastable dynamics for hyperbolic variations of the Allen–Cahn equation
2017
Communications in Mathematical Sciences
Metastable dynamics of a hyperbolic variation of the Allen-Cahn equation with homogeneous Neumann boundary conditions are considered. Using the "dynamical approach" proposed by Carr-Pego [10] and Fusco-Hale [19] to study slow-evolution of solutions in the classic parabolic case, we prove existence and persistence of metastable patterns for an exponentially long time. In particular, we show the existence of an "approximately invariant" N-dimensional manifold ℳ_0 for the hyperbolic Allen-Cahn
doi:10.4310/cms.2017.v15.n7.a12
fatcat:ov3wuo2ujffjpidrg3y3g3zela