Transition layer for the heterogeneous Allen-Cahn equation
From MaRDI portal
Publication:930022
DOI10.1016/j.anihpc.2007.03.008zbMath1148.35030arXivmath/0702878OpenAlexW2080428609MaRDI QIDQ930022
Andrea Malchiodi, Fethi Mahmoudi, Wei, Juncheng
Publication date: 19 June 2008
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0702878
Asymptotic behavior of solutions to PDEs (35B40) Nonlinear boundary value problems for linear elliptic equations (35J65) Asymptotic expansions of solutions to PDEs (35C20) Resonance in context of PDEs (35B34)
Related Items (16)
Phase transition layers for Fife-Greenlee problem on smooth bounded domain ⋮ Clustering of boundary interfaces for an inhomogeneous Allen-Cahn equation on a smooth bounded domain ⋮ Connectivity of boundaries by clustering phase transition layers of Fife-Greenlee problem on smooth bounded domain ⋮ Locations of interior transition layers to inhomogeneous transition problems in higher -dimensional domains ⋮ Radial and bifurcating non-radial solutions for a singular perturbation problem in the case of exchange of stabilities ⋮ A review on singularly perturbed differential equations with turning points and interior layers ⋮ Phase transition layers with boundary intersection for an inhomogeneous Allen-Cahn equation ⋮ The heterogeneous Allen-Cahn equation in a ball: Solutions with layers and spikes ⋮ MINIMAX PROBABILITIES FOR AUBRY–MATHER PROBLEMS ⋮ On the Profile of Globally and Locally Minimizing Solutions of the Spatially Inhomogeneous Allen–Cahn and Fisher–KPP Equations ⋮ Resonance Phenomena in a Singular Perturbation Problem in the Case of Exchange of Stabilities ⋮ Stable transition layers in an unbalanced bistable equation ⋮ Patterns in a balanced bistable equation with heterogeneous environments on surfaces of revolution ⋮ Concentration of Solutions for Some Singularly Perturbed Neumann Problems ⋮ Stable Transition Layers to Singularly Perturbed Spatially Inhomogeneous Allen-Cahn Equation ⋮ The ground state of a Gross-Pitaevskii energy with general potential in the Thomas-Fermi limit
Cites Work
- Unnamed Item
- Unnamed Item
- Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains
- Concentration on minimal submanifolds for a singularly perturbed Neumann problem
- On the singular limit in a phase field model of phase transitions
- Construction and stability analysis of transition layer solutions in reaction-diffusion systems
- Boundary-clustered interfaces for the Allen-Cahn equation
- Stable transition layers in a semilinear boundary value problem
- Boundary and interior transition layer phenomena for pairs of second- order differential equations
- Singular perturbations as a selection criterion for periodic minimizing sequences
- Connectivity of phase boundaries in strictly convex domains
- Multi-layer solutions for an elliptic problem.
- Motion of a droplet by surface tension along the boundary
- From constant mean curvature hypersurfaces to the gradient theory of phase transitions.
- Perturbation theory for linear operators.
- Clustering layers and boundary layers in spatially inhomogeneous phase transition problems.
- Stable transition layers in a semilinear diffusion equation with spatial inhomogeneities in \(N\)-dimensional domains
- Multi-layered stationary solutions for a spatially inhomogeneous Allen--Cahn equation.
- Solutions concentrating at curves for some singularly perturbed elliptic problems
- Multidimensional boundary layers for a singularly perturbed Neumann problem
- Mixed states for an Allen-Cahn type equation. II
- Construction of various types of solutions for an elliptic problem
- Morse index of layered solutions to the heterogeneous Allen-Cahn equation
- Boundary interface for the Allen-Cahn equation
- On the existence and Morse index of solutions to the Allen-Cahn equation in two dimensions
- Concentration on curves for nonlinear Schrödinger Equations
- Resonance and Interior Layers in an Inhomogeneous Phase Transition Model
- Stability of Singularly Perturbed Solutions to Systems of Reaction-Diffusion Equations
- A variational approach for a class of singular perturbation problems and applications
- Existence and stability of transition layers
- Local minimisers and singular perturbations
- Layers With Nonsmooth Interface in a Semilinear Elliptic Problem
- INTERIOR TRANSITION LAYERS FOR ELLIPTIC BOUNDARY VALUE PROBLEMS WITH A SMALL PARAMETER
- Periodic traveling waves and locating oscillating patterns in multidimensional domains
- On the convergence of stable phase transitions
- Solutions to the Nonautonomous Bistable Equation with Specified Morse Index. Part I: Existence
- Mixed states for an Allen‐Cahn type equation
- Boundary concentration phenomena for a singularly perturbed elliptic problem
- Radially Symmetric Internal Layers in a Semilinear Elliptic System
- Higher energy solutions in the theory of phase transitions: A variational approach
This page was built for publication: Transition layer for the heterogeneous Allen-Cahn equation
