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.
Bellettini, G., De Masi, A., Dirr, N., Presutti, E. (2007). Stability of invariant manifolds in one and two dimensions. NONLINEARITY, 20(3), 537-582 [10.1088/0951-7715/20/3/002].
Stability of invariant manifolds in one and two dimensions
BELLETTINI, GIOVANNI;PRESUTTI, ERRICO
2007-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
