JournalsifbVol. 23, No. 2pp. 169–190

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

  • Masashi Mizuno

    Nihon University, Tokyo, Japan
  • Keisuke Takasao

    Kyoto University, Japan
A curve shortening equation with time-dependent mobility related to grain boundary motions cover
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Abstract

A curve shortening equation related to the evolution of grain boundaries is presented. This equation is derived from the grain boundary energy by applying the maximum dissipation principle. Gradient estimates and large time asymptotic behavior of solutions are considered. In the proof of these results, one key ingredient is a new weighted monotonicity formula that incorporates a time-dependent mobility.

Cite this article

Masashi Mizuno, Keisuke Takasao, A curve shortening equation with time-dependent mobility related to grain boundary motions. Interfaces Free Bound. 23 (2021), no. 2, pp. 169–190

DOI 10.4171/IFB/453