Geodesic
The effective energy in the Allen–Cahn model with deformation
M. Šilhavý1
1Czech Academy of Sciences, Prague, Czech Republic
Interfaces and free boundaries, Tome 13 (2011) no. 2, pp. 255-270

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DOI

The sharp interface limit of a diffuse interface theory of phase transitions is considered in static situations. The diffuse interface model is of the Allen–Cahn type with deformation, with a parameter ε measuring the width of the interface. Equilibrium states of a given elongation and a given interface width are considered and the asymptotics for ε→0 of the equilibrium energy is determined. The interface energy is defined as the excess energy over the corresponding two phase state with a sharp interface without the interface energy. It is shown that to within the term of order o(ε) the interface energy is equal to σε where the coefficient σ is given by a new formula that involves the mechanical contribution to the total energy. Also the corresponding equilibrium states are determined and shown to converge to a sharp interface state for ε→0.
DOI : 10.4171/ifb/257
Classification : 74-XX, 49-XX, 00-XX
Mots-clés : phase transitions; diffuse and sharp phase interface; interfacial energy

M. Šilhavý  1

1 Czech Academy of Sciences, Prague, Czech Republic 
M. Šilhavý. The effective energy in the Allen–Cahn model with deformation. Interfaces and free boundaries, Tome 13 (2011) no. 2, pp. 255-270. doi: 10.4171/ifb/257
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     title = {The effective energy in the {Allen{\textendash}Cahn} model with deformation},
     journal = {Interfaces and free boundaries},
     pages = {255--270},
     year = {2011},
     volume = {13},
     number = {2},
     doi = {10.4171/ifb/257},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/257/}
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