TY - JOUR
T1 - Evolution of grain boundaries
AU - Kinderlehrer, David
AU - Liu, Chun
N1 - Funding Information:
This work was supported by the MRSEC program of the NSF under Award DMR 0079996 and through Center for Nonlinear Analysis NSF Grant DMS-9303054. David Kinderlehrer is also supported by ARO DAAH Grant 04 96 0060 and NSF Grant DMS-0072194. Chun Liu is supported by NSF Grant DMS-9972040.
PY - 2001/6
Y1 - 2001/6
N2 - Evolution and trend to equilibrium of a (planar) network of grain boundaries subject to curvature driven growth is established under the assumption that the system is initially close to some equilibrium configuration. Curvature driven growth is the primary mechanism in processing polycrystalline materials to achieve desired texture, ductility, toughness, strength, and other properties. Imposition of the Herring condition at triple junctions ensures that this system is dissipative and that the complementing conditions hold. We introduce a new way to employ the known Solonnikov-type estimates, which are only local in time, to obtain solutions that are global in time with controlled norm. These issues were raised as part of the Mesoscale Interface Mapping Project.
AB - Evolution and trend to equilibrium of a (planar) network of grain boundaries subject to curvature driven growth is established under the assumption that the system is initially close to some equilibrium configuration. Curvature driven growth is the primary mechanism in processing polycrystalline materials to achieve desired texture, ductility, toughness, strength, and other properties. Imposition of the Herring condition at triple junctions ensures that this system is dissipative and that the complementing conditions hold. We introduce a new way to employ the known Solonnikov-type estimates, which are only local in time, to obtain solutions that are global in time with controlled norm. These issues were raised as part of the Mesoscale Interface Mapping Project.
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U2 - 10.1142/S0218202501001069
DO - 10.1142/S0218202501001069
M3 - Article
AN - SCOPUS:0345860864
SN - 0218-2025
VL - 11
SP - 713
EP - 729
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
IS - 4
ER -