A homogenization result in the gradient theory of phase transitions
From MaRDI portal
Publication:2335844
DOI10.4171/IFB/426zbMath1425.74389arXiv1808.01972MaRDI QIDQ2335844
Cristina Popovici, Riccardo Cristoferi, Adrian Hagerty, Irene Fonseca
Publication date: 15 November 2019
Published in: Interfaces and Free Boundaries (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1808.01972
Variational problems in a geometric measure-theoretic setting (49Q20) Homogenization in equilibrium problems of solid mechanics (74Q05) Phase transitions (general) in equilibrium statistical mechanics (82B26)
Related Items (12)
Anisotropic surface tensions for phase transitions in periodic media ⋮ Homogenization of the Allen-Cahn equation with periodic mobility ⋮ Homogenization and phase separation with space dependent wells: the subcritical case ⋮ The Ginzburg-Landau energy with a pinning term oscillating faster than the coherence length ⋮ Calculus of variations. Abstracts from the workshop held August 14--20, 2022 ⋮ Gradient Damage Models for Heterogeneous Materials ⋮ Γ-convergence and stochastic homogenisation of phase-transition functionals ⋮ Asymptotic behavior of the capacity in two-dimensional heterogeneous media ⋮ Variational homogenization: old and new ⋮ Sharp interface limit of a multi-phase transitions model under nonisothermal conditions ⋮ Topological singularities in periodic media: Ginzburg-Landau and core-radius approaches ⋮ Phase separation in heterogeneous media
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Relaxation of quasiconvex functionals in \(BV(\Omega, \mathbb{R}^ N)\) for integrands \(f(x, u, \bigtriangledown u)\)
- Singular perturbations of variational problems arising from a two-phase transition model
- Minimal interface criterion for phase transitions in mixtures of Cahn- Hilliard fluids
- Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy
- Homogenization of nonconvex integral functionals and cellular elastic materials
- Gradient theory of phase transitions with boundary contact energy
- The effect of a singular perturbation on nonconvex variational problems
- On the relaxation in \(BV(\Omega ;\mathbb{R}^ m)\) of quasi-convex integrals
- Periodic solutions and homogenization of non linear variational problems
- A global method for relaxation
- An introduction to \(\Gamma\)-convergence
- Homogenization of Cahn-Hilliard-type equations via evolutionary \(\Gamma\)-convergence
- The gradient theory of phase transitions and the minimal interface criterion
- \(\Gamma\)-convergence of the Allen-Cahn energy with an oscillating forcing term
- Minimizers and gradient flows for singularly perturbed bi-stable potentials with a Dirichlet condition
- Nonlocal character of the reduced theory of thin films with higher order perturbations
- Gradient theory of phase transitions with a rapidly oscillating forcing term
- The gradient theory of phase transitions for systems with two potential wells
- Local minimisers and singular perturbations
- Quasi-Convex Integrands and Lower Semicontinuity in $L^1 $
- Combined effects of homogenization and singular perturbations in elasticity.
- Anisotropic singular perturbations—the vectorial case
- Gradient theory of phase transitions in composite media
- A Γ‐convergence result for the two‐gradient theory of phase transitions
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
This page was built for publication: A homogenization result in the gradient theory of phase transitions
