Energy dissipative solutions to the Kobayashi–Warren–Carter system

DOI10.1088/1361-6544/aa6eb4zbMath1386.35250arXiv1702.04033OpenAlexW3102794050MaRDI QIDQ4978484

Ken Shirakawa, Salvador Moll, Hiroshi Watanabe

Publication date: 11 August 2017

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.04033

zbMATH Keywords

regularityenergy dissipation\(\Gamma\)-convergenceparabolic systemgrain boundary motion\(\omega\)-limit

Mathematics Subject Classification ID

Singular parabolic equations (35K67) PDEs with measure (35R06) Unilateral problems for parabolic systems and systems of variational inequalities with parabolic operators (35K87)

Related Items (8)

Constrained optimization problems governed by PDE models of grain boundary motions ⋮ A finer singular limit of a single-well Modica-Mortola functional and its applications to the Kobayashi-Warren-Carter energy ⋮ Numerical solution of a phase field model for polycrystallization processes in binary mixtures ⋮ Kobayashi-Warren-Carter system of singular type under dynamic boundary condition ⋮ Optimal control problems governed by 1-D Kobayashi-Warren-Carter type systems ⋮ Kobayashi-Warren-Carter type systems with nonhomogeneous Dirichlet boundary data for crystalline orientation ⋮ Solvability for the non-isothermal Kobayashi-Warren-Carter system ⋮ Large-time behavior for a PDE model of isothermal grain boundary motion with a constraint

Cites Work

• Large-time behavior for a PDE model of isothermal grain boundary motion with a constraint
• Global solvability of a model for grain boundary motion with constraint
• Very singular diffusion equations: second and fourth order problems
• A phase-field model of grain boundary motion.
• Compact sets in the space \(L^ p(0,T;B)\)
• Equations with singular diffusivity
• A continuum model of grain boundaries
• A notion of total variation depending on a metric with discontinuous coefficients
• Solvability of one-dimensional phase field systems associated with grain boundary motion
• Energy-dissipative solution to a one-dimensional phase field model of grain boundary motion
• A relaxation result in BV for integral functionals with discontinuous integrands
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