Geodesic
Action minimization and macroscopic interface motion under forced displacement
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 765-792

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We study an one dimensional model where an interface is the stationary solution of a mesoscopic non local evolution equation which has been derived by a microscopic stochastic spin system. Deviations from this evolution equation can be quantified by obtaining the large deviations cost functional from the underlying stochastic process. For such a functional, derived in a companion paper, we investigate the optimal way for a macroscopic interface to move from an initial to a final position distant by R within fixed time T. We find that for small values of R∕T the interface moves with a constant speed, while for larger values there appear nucleations of the other phase ahead of the front.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2017021
Classification : 82C24, 49J
Keywords: Action minimization, large deviations functional, sharp-interface limit, non-local Allen−Cahn equation, nucleation

Birmpa, Panagiota 1 ; Tsagkarogiannis, Dimitrios 1

1 
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     title = {Action minimization and macroscopic interface motion under forced displacement},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {765--792},
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Birmpa, Panagiota; Tsagkarogiannis, Dimitrios. Action minimization and macroscopic interface motion under forced displacement. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 765-792. doi: 10.1051/cocv/2017021

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