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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 20
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 5, October 2013
  4. A two-gradient approach for phase transitions in thin films
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 6, December 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 5, October 2013
Periodic solutions in general scalar non-autonomous models with delays
On the stability of travelling waves with vorticity obtained by minimization
A two-gradient approach for phase transitions in thin films
A priori estimates for a class of degenerate elliptic equations
P-Laplacian problems with nonlinearities interacting with the spectrum
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 4, August 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 3, June 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 2, April 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 1, February 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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A two-gradient approach for phase transitions in thin films

Content Provider SpringerLink
Author Millot, Vincent Galvão Sousa, Bernardo
Copyright Year 2013
Abstract Motivated by solid-solid phase transitions in elastic thin films, we perform a Γ-convergence analysis for a singularly perturbed energy related to second order phase transitions in a domain of vanishing thickness. Under a two-wells assumption, we derive a sharp interface model with an interfacial energy depending on the asymptotic ratio between the characteristic length scale of the phase transition and the thickness of the film. In each case, the interfacial energy is determined by an explicit optimal profile problem. This asymptotic problem entails a nontrivial dependance on the thickness direction when the phase transition is created at the same rate as the thin film, while it shows a separation of scales if the thin film is created at a faster rate than the phase transition. The last regime, when the phase transition is created at a faster rate than the thin film, is more involved. Depending on growth conditions of the potential and the compatibility of the two phases, we either obtain a sharp interface model with scale separation, or a trivial situation driven by rigidity effects.
Ending Page 1682
Page Count 52
Starting Page 1631
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 5
Volume Number 20
Language English
Publisher Springer Basel
Publisher Date 2013-03-12
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Thin films Methods involving semicontinuity and convergence; relaxation Analysis Singular perturbations Γ-convergence Variational methods including variational inequalities Phase transitions Double-well potential Problems involving partial differential equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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