A curve shortening equation with time-dependent mobility related to grain boundary motions

DOI10.4171/IFB/453zbMath1483.53109arXiv2002.01617OpenAlexW3197221262MaRDI QIDQ2244859

Keisuke Takasao, Masashi Mizuno

Publication date: 12 November 2021

Published in: Interfaces and Free Boundaries (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.01617

zbMATH Keywords

curve shortening equationgrain boundary motionweighted monotonicity formula

Mathematics Subject Classification ID

Variational methods for problems in mechanics (70G75) Analysis of microstructure in solids (74N15) Moving boundary problems for PDEs (35R37) Flows related to mean curvature (53E10)

Cites Work

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• Asymptotic behavior for singularities of the mean curvature flow
• Mean curvature evolution of entire graphs
• Interior estimates for hypersurfaces moving by mean curvature
• Interior curvature estimates for hypersurfaces of prescribed mean curvature
• Large time asymptotic behavior of grain boundaries motion with dynamic lattice misorientations and with triple junctions drag
• Gradient estimates for mean curvature flow with Neumann boundary conditions
• Gradient estimates and existence of mean curvature flow with transport term.
• Asymptotically self‐similar blow‐up of semilinear heat equations
• EVOLUTION OF GRAIN BOUNDARIES
• Sharp estimates for mean curvature flow of graphs
• Motion of Grain Boundaries with Dynamic Lattice Misorientations and with Triple Junctions Drag

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