Stability analysis for Allen-Cahn type equation associated with the total variation energy

DOI10.1016/j.na.2004.08.030zbMath1274.35083OpenAlexW2020527596MaRDI QIDQ707222

Ken Shirakawa, Masato Kimura

Publication date: 9 February 2005

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2004.08.030

zbMATH Keywords

total variationstability analysisAllen-Cahn type equation

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Variational methods for second-order elliptic equations (35J20) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50)

Related Items (10)

Constrained optimization problems governed by PDE models of grain boundary motions ⋮ An augmented Lagrangian model for signal segmentation ⋮ Lagrange multiplier and singular limit of double obstacle problems for the Allen-Cahn equation with constraint ⋮ A phase-field model for articular cartilage regeneration in degradable scaffolds ⋮ Weak solutions for unidirectional gradient flows: existence, uniqueness, and convergence of time discretization schemes ⋮ Optimal control problems governed by 1-D Kobayashi-Warren-Carter type systems ⋮ Remarks on numerical experiments of the Allen-Cahn equations with constraint via Yosida approximation ⋮ On boundary detachment phenomena for the total variation flow with dynamic boundary conditions ⋮ Very singular diffusion equations: second and fourth order problems ⋮ Singular limit of Allen-Cahn equation with constraint and its Lagrange multiplier

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