Limiting classification on linearized eigenvalue problems for 1-dimensional Allen-Cahn equation. II: Asymptotic profiles of eigenfunctions.

DOI10.1016/j.jde.2016.08.016zbMath1355.34091OpenAlexW2507459598MaRDI QIDQ324564

Shoji Yotsutani, Tohru Wakasa

Publication date: 17 October 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2016.08.016

zbMATH Keywords

Floquet theoryAllen-Cahn equationasymptotic formulas of eigenfunctionsasymptotic formulas of eigenvalueslinearized eigenvalue problems

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15) Asymptotic expansions of solutions to ordinary differential equations (34E05) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items (5)

Representation formulas of solutions and bifurcation sheets to a nonlocal Allen-Cahn equation ⋮ Asymptotic formulas of the eigenvalues for the linearization of a one-dimensional sinh-Poisson equation ⋮ All global bifurcation diagrams of stationary solutions to a phase field model ⋮ Exact eigenvalues and eigenfunctions for a one-dimensional Gel’fand problem ⋮ Limiting classification on linearized eigenvalue problems for 1-dimensional Allen-Cahn equation. I. Asymptotic formulas of eigenvalues

Cites Work

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• Geometric theory of semilinear parabolic equations
• Slow-motion manifolds, dormant instability, and singular perturbations
• Limiting classification on linearized eigenvalue problems for 1-dimensional Allen-Cahn equation. I. Asymptotic formulas of eigenvalues
• A bifurcation problem for a nonlinear partial differential equation of parabolic type^†
• Metastable patterns in solutions of u_t = ϵ²u_xx − f(u)

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