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EnglishWe 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 L2 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.
http://hdl.handle.net/11697/7681| Titolo: | Stability of invariant manifolds in one and two dimensions |
| Autori interni: | DE MASI, Anna |
| Data di pubblicazione: | 2007 |
| Rivista: | NONLINEARITY |
| 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 L2 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. |
| Handle: | http://hdl.handle.net/11697/7681 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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