The Toda system and clustering interfaces in the Allen-Cahn equation
From MaRDI portal
Publication:1000544
DOI10.1007/s00205-008-0143-3zbMath1163.35017OpenAlexW2169577913MaRDI QIDQ1000544
Michał Kowalczyk, Manuel A. del Pino, Wei, Juncheng
Publication date: 9 February 2009
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00205-008-0143-3
Asymptotic behavior of solutions to PDEs (35B40) Nonlinear elliptic equations (35J60) Theoretical approximation in context of PDEs (35A35) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38)
Related Items
On Ambrosetti-Malchiodi-Ni conjecture on two-dimensional smooth bounded domains: clustering concentration layers ⋮ A counterexample to a conjecture by De Giorgi in large dimensions ⋮ Singular solutions of Toda system in high dimensions ⋮ Nondegeneracy of the traveling lump solution to the 2 + 1 Toda lattice ⋮ Phase transition layers for Fife-Greenlee problem on smooth bounded domain ⋮ Interface foliation near minimal submanifolds in Riemannian manifolds with positive Ricci curvature ⋮ 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 ⋮ Nearly parallel vortex filaments in the 3D Ginzburg-Landau equations ⋮ Interfaces with boundary intersection for an inhomogeneous Allen-Cahn equation in three-dimensional case ⋮ Interior interfaces with (or without) boundary intersection for an anisotropic Allen-Cahn equation ⋮ Ancient shrinking spherical interfaces in the Allen-Cahn flow ⋮ Double-well phase transitions are more rigid than minimal hypersurfaces ⋮ The p-widths of a surface ⋮ Interface foliation for an inhomogeneous Allen-Cahn equation in Riemannian manifolds ⋮ Solutions with single radial interface of the generalized Cahn-Hilliard flow ⋮ On stable and finite Morse index solutions of the fractional Toda system ⋮ On De Giorgi's conjecture in dimension \(N\geq 9\) ⋮ Phase transition layers with boundary intersection for an inhomogeneous Allen-Cahn equation ⋮ LAYERED SOLUTIONS WITH CONCENTRATION ON LINES IN THREE-DIMENSIONAL DOMAINS ⋮ Catenoidal layers for the Allen-Cahn equation in bounded domains ⋮ Standing pulse solutions to FitzHugh-Nagumo equations ⋮ The Toda system and multiple-end solutions of autonomous planar elliptic problems ⋮ Recent progress on stable and finite Morse index solutions of semilinear elliptic equations ⋮ Clustering phase transition layers with boundary intersection for an inhomogeneous Allen-Cahn equation ⋮ Some new entire solutions of semilinear elliptic equations on \(\mathbb R^n\) ⋮ Stable and finite Morse index solutions of Toda system ⋮ Multiple-end solutions to the Allen-Cahn equation in \(\mathbb R^2\) ⋮ Second order estimate on transition layers ⋮ Interacting helical vortex filaments in the three-dimensional Ginzburg-Landau equation ⋮ Plateau's Problem as a Singular Limit of Capillarity Problems ⋮ Curve-Like Concentration Layers for a Singularly Perturbed Nonlinear Problem with Critical Exponents ⋮ The ground state of a Gross-Pitaevskii energy with general potential in the Thomas-Fermi limit
Cites Work
- Unnamed Item
- Boundary-clustered interfaces for the Allen-Cahn equation
- The effect of a singular perturbation on nonconvex variational problems
- The solution to a generalized Toda lattice and representation theory
- Asymptotic behavior and stability of solutions of semilinear diffusion equations
- Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics
- Generation and propagation of interfaces for reaction-diffusion equations
- Ginzburg-Landau equation and motion by mean curvature. I: Convergence
- Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
- Connectivity of phase boundaries in strictly convex domains
- ``Bubble-tower radial solutions in the slightly supercritical Brezis-Nirenberg problem.
- Motion of a droplet by surface tension along the boundary
- Multiple clustered layer solutions for semilinear Neumann problems on a ball
- From constant mean curvature hypersurfaces to the gradient theory of phase transitions.
- The gradient theory of phase transitions and the minimal interface criterion
- Clustering layers and boundary layers in spatially inhomogeneous phase transition problems.
- Multi-layered stationary solutions for a spatially inhomogeneous Allen--Cahn equation.
- Multidimensional boundary layers for a singularly perturbed Neumann problem
- Generalized motion by mean curvature with Neumann conditions and the Allen-Cahn model for phase transitions
- On the existence of high multiplicity interfaces
- Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory.
- Closed geodesics on oval surfaces and pattern formation
- On the existence and Morse index of solutions to the Allen-Cahn equation in two dimensions
- THE GIERER & MEINHARDT SYSTEM: THE BREAKING OF HOMOCLINICS AND MULTI-BUMP GROUND STATES
- Eponential Decay To Stable States In Phase Transitions Via A Double Log–Transformation
- Concentration on curves for nonlinear Schrödinger Equations
- Fast Reaction, Slow Diffusion, and Curve Shortening
- Local minimisers and singular perturbations
- Phase transitions and generalized motion by mean curvature
- On the convergence of stable phase transitions
- Slow Dynamics of Interfaces in the Allen--Cahn Equation on a Strip-like Domain
- An elementary construction of complex patterns in nonlinear Schr$ouml$dinger equations
- Boundary concentration phenomena for a singularly perturbed elliptic problem
- Phase field model with a variable chemical potential
- Uniform convergence of a singular perturbation problem
- Geometrical Evolution of Developed Interfaces
- On interacting bumps of semi-classical states of nonlinear Schrödinger equations.