Invariant manifolds for metastable patterns in u t = ε 2 u xx — f ( u )

Source abstract

Synopsis We consider the above equation on the interval 0 ≦ x ≦ 1 subject to Neumann boundary conditions with f ( u ) = F ′( u ) where F is a double well energy density function with equal minima. Our previous work [3] proved the existence and persistence of very slowly evolving patterns (metastable states) in solutions with two-phase initial data. Here we characterise these metastable states in terms of the global unstable manifolds of equilibria, as conjectured by Fusco and Hale [6].