Stationary solutions to the one-dimensional Cahn-Hilliad equations: Proof by the complete elliptic integrals

DOI10.3934/dcds.2007.19.609zbMath1162.34014OpenAlexW2091152264MaRDI QIDQ951277

Satoshi Kosugi, Shoji Yotsutani, Yoshihisa Morita

Publication date: 23 October 2008

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2007.19.609

zbMATH Keywords

exact solutionnonlinear differential equationnon-local boundary value problem

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Bifurcation theory for ordinary differential equations (34C23) Explicit solutions, first integrals of ordinary differential equations (34A05) Elliptic functions and integrals (33E05)

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Exact multiplicity of stationary limiting problems of a cell polarization model ⋮ On a generalized Cahn-Hilliard model with \(p\)-Laplacian ⋮ Nonlocal eigenvalue problems arising in a generalized phase-field-type system ⋮ Representation formulas of solutions and bifurcation sheets to a nonlocal Allen-Cahn equation ⋮ All global bifurcation diagrams of stationary solutions to a phase field model ⋮ Limiting classification on linearized eigenvalue problems for 1-dimensional Allen-Cahn equation. I. Asymptotic formulas of eigenvalues ⋮ Global bifurcation sheet and diagrams of wave-pinning in a reaction-diffusion model for cell polarization

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