Singular limit of Allen-Cahn equation with constraint and its Lagrange multiplier

DOI10.3934/proc.2015.0418zbMath1381.35090OpenAlexW2596143350MaRDI QIDQ260809

Noriaki Yamazaki, Mohammad Hassan Farshbaf-Shaker, Takeshi Fukao

Publication date: 22 March 2016

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

Full work available at URL: https://doi.org/10.3934/proc.2015.0418

zbMATH Keywords

Lagrange multipliersubdifferentialconstraintsingular limitAllen-Cahn equationdouble obstacle

Mathematics Subject Classification ID

PDEs with multivalued right-hand sides (35R70) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Initial-boundary value problems for second-order parabolic equations (35K20) Free boundary problems for PDEs (35R35) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26)

Related Items (3)

Lagrange multiplier and singular limit of double obstacle problems for the Allen-Cahn equation with constraint ⋮ Remarks on numerical experiments of the Allen-Cahn equations with constraint via Yosida approximation ⋮ New approximate method for the Allen-Cahn equation with double-obstacle constraint and stability criteria for numerical simulations

Cites Work

• Optimal control problem for Allen-Cahn type equation associated with total variation energy
• Attractors of nonlinear evolution systems generated by time-dependent subdifferentials in Hilbert spaces
• Stability analysis for Allen-Cahn type equation associated with the total variation energy
• Nonmonotone perturbations for nonlinear parabolic equations associated with subdifferential operators, Cauchy problems
• Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics
• Integrality of varifolds in the singular limit of reaction-diffusion equations
• Convexity and Optimization in Banach Spaces
• Lagrange Multiplier Approach to Variational Problems and Applications
• Asymptotics for a parabolic double obstacle problem
• Primal‐dual active set methods for Allen–Cahn variational inequalities with nonlocal constraints
• Perturbations of nonlinear maximal monotone sets in banach space
• Nonlinear Differential Equations of Monotone Types in Banach Spaces
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