Symmetry of Entire Solutions to the Allen-Cahn Equation

DOI10.1515/ans-2015-0304zbMath1333.35019OpenAlexW2511317110MaRDI QIDQ5500258

Fang Zhang, Changfeng Gui

Publication date: 5 August 2015

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ans-2015-0304

zbMATH Keywords

symmetrylevel setentire solutionAllen-Cahn equationHamiltonian identity

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Nonlinear elliptic equations (35J60) Variational methods for second-order elliptic equations (35J20) Entire solutions to PDEs (35B08) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (1)

Axial symmetry of some steady state solutions to nonlinear Schrödinger equations

Cites Work

• Unnamed Item
• Existence and global stability of traveling curved fronts in the Allen-Cahn equations
• Nontrivial large-time behaviour in bistable reaction-diffusion equations
• Asymptotic properties and classification of bistable fronts with Lipschitz level sets
• Global stability of traveling curved fronts in the Allen-Cahn equations
• A gradient bound and a liouville theorem for nonlinear poisson equations
• Entire solutions of the KPP equation
• Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
• Stability of travelling waves in a model for conical flames in two space dimensions
• Traveling Fronts of Pyramidal Shapes in the Allen–Cahn Equations
• Multidimensional stability of planar travelling waves

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