Global solution branches for a nonlocal Allen-Cahn equation

DOI10.1016/j.jde.2018.01.025zbMath1387.34034OpenAlexW2791638255MaRDI QIDQ1701868

Shoji Yotsutani, Tatsuki Mori, Kousuke Kuto, Tohru Tsujikawa

Publication date: 27 February 2018

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

Full work available at URL: https://doi.org/10.1016/j.jde.2018.01.025

zbMATH Keywords

monotonicitybifurcationnonlocal termAllen-Cahn equationlevel set analysis

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Parameter dependent boundary value problems for ordinary differential equations (34B08) Nonlocal and multipoint boundary value problems for ordinary differential equations (34B10)

Related Items (6)

Secondary bifurcation for a nonlocal Allen-Cahn equation ⋮ Stability for stationary solutions of a nonlocal Allen-Cahn equation ⋮ Families of rational and semirational solutions of the partial reverse space-time nonlocal Mel'nikov equation ⋮ 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 ⋮ Existence of spiky stationary solutions to a mass-conserved reaction-diffusion model

Cites Work

• Exact multiplicity of stationary limiting problems of a cell polarization model
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• Stationary Fix-Caginalp equation with non-local term
• Global bifurcation of steady-state solutions
• Global solution branches of two point boundary value problems
• Bifurcation, perturbation of simple eigenvalues, and linearized stability
• Secondary bifurcation for a nonlocal Allen-Cahn equation
• Asymptotic and Bifurcation Analysis of Wave-Pinning in a Reaction-Diffusion Model for Cell Polarization
• A bifurcation problem for a nonlinear partial differential equation of parabolic type^†
• Semilinear Neumann boundary value problems on a rectangle
• Asymptotic behavior of solutions of an allen-cahn equation with a nonlocal term

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