Abstract
We consider the gradient flow associated with a nonlocal free energy functional and extend to such a case results obtained for the Allen-Cahn equation on 'slow motions on invariant manifolds'. The manifolds in question are time-invariant one-dimensional curves in an L-2 space which connect the two ground states ( interpreted as the pure phases of the system) to the first excited state ( interpreted as a diffuse interface). Local and structural stability of the manifolds are proved and applications to the characterization of optimal tunnelling are discussed.
| Original language | English |
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| Pages (from-to) | 537-582 |
| Number of pages | 46 |
| Journal | Nonlinearity |
| Volume | 20 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2007 |