Communications in Mathematical Sciences

Volume 19 (2021)

Number 5

Large time asymptotic behavior of grain boundaries motion with dynamic lattice misorientations and with triple junctions drag

Pages: 1403 – 1428



Yekaterina Epshteyn (Department of Mathematics, University of Utah, Salt Lake City, Ut., U.S.A.)

Chun Liu (Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Il., U.S.A.)

Masashi Mizuno (Department of Mathematics, College of Science and Technology, Nihon University, Tokyo, Japan)


Many technologically useful materials are polycrystals composed of a myriad of small monocrystalline grains separated by grain boundaries. Dynamics of grain boundaries play an essential role in defining the material’s properties across multiple scales. In this work, we study the largetime asymptotic behavior of the model for the motion of grain boundaries with the dynamic lattice misorientations and the triple junctions drag.


grain growth, grain boundary network, texture development, lattice misorientation, triple junction drag, energetic variational approach, geometric evolution equations, large-time asymptotics

2010 Mathematics Subject Classification

35R37, 49Q20, 53C44, 74N15

Received 5 March 2020

Accepted 13 January 2021

Published 7 July 2021