Evolution of grain boundaries

David Kinderlehrer, Chun Liu

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)713-729
Number of pages17
JournalMathematical Models and Methods in Applied Sciences
Issue number4
StatePublished - Jun 2001

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Applied Mathematics


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