The effective energy in the Allen-Cahn model with deformation

0360202 - MÚ 2012 RIV US eng J - Journal Article
Šilhavý, Miroslav
The effective energy in the Allen-Cahn model with deformation.
Interfaces and Free Boundaries. Roč. 13, č. 2 (2011), s. 255-270. ISSN 1463-9963. E-ISSN 1463-9971
Institutional research plan: CEZ:AV0Z10190503
Keywords : phase transitions * diffuse and sharp phase interface * interfacial energy
Subject RIV: BA - General Mathematics
Impact factor: 0.795, year: 2011
http://www.ems-ph.org/journals/show_abstract.php?issn=1463-9963&vol=13&iss=2&rank=5

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 measuring the width of the interface. Equilibrium states of a given elongation and a given interface width are considered and the asymptotics for the width tending to zero is determined. It is shown that to within the term of higher order than the width of the interface, the interface energy is proportional to the width where the coefficient is given by a new formula that involves the mechanical contribution to the total energy.
Permanent Link: http://hdl.handle.net/11104/0197812