Large-time behavior for a PDE model of isothermal grain boundary motion with a constraint

DOI10.3934/proc.2015.1009zbMath1343.35030OpenAlexW2324877277MaRDI QIDQ260947

Hiroshi Watanabe, Ken Shirakawa

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.2015.1009

zbMATH Keywords

subdifferential\(\Gamma\)-convergenceweighted total variation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order parabolic equations (35K20) Singular parabolic equations (35K67) Unilateral problems for parabolic systems and systems of variational inequalities with parabolic operators (35K87)

Related Items (5)

Kobayashi-Warren-Carter system of singular type under dynamic boundary condition ⋮ Optimal control problems governed by 1-D Kobayashi-Warren-Carter type systems ⋮ Energy dissipative solutions to the Kobayashi–Warren–Carter system ⋮ Kobayashi-Warren-Carter type systems with nonhomogeneous Dirichlet boundary data for crystalline orientation ⋮ Solvability for the non-isothermal Kobayashi-Warren-Carter system

Cites Work

• Existence of solutions to the Kobayashi-Warren-Carter system
• Compact sets in the space \(L^ p(0,T;B)\)
• An introduction to \(\Gamma\)-convergence
• 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
• Phase-field systems for grain boundary motions under isothermal solidifications
• Energy dissipative solutions to the Kobayashi–Warren–Carter system
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