Geodesic
A curve shortening equation with time-dependent mobility related to grain boundary motions
Masashi Mizuno1 ; Keisuke Takasao2
1Nihon University, Tokyo, Japan
2Kyoto University, Japan
Interfaces and free boundaries, Tome 23 (2021) no. 2, pp. 169-190

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DOI

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.
DOI : 10.4171/ifb/453
Classification : 53-XX, 35-XX, 70-XX, 74-XX
Mots-clés : Grain boundary motion, curve shortening equation, weighted monotonicity formula

Masashi Mizuno  1   ; Keisuke Takasao  2

1 Nihon University, Tokyo, Japan
2 Kyoto University, Japan 
Masashi Mizuno; Keisuke Takasao. A curve shortening equation with time-dependent mobility related to grain boundary motions. Interfaces and free boundaries, Tome 23 (2021) no. 2, pp. 169-190. doi: 10.4171/ifb/453
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     title = {A curve shortening equation with time-dependent mobility related to grain boundary motions},
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     pages = {169--190},
     year = {2021},
     volume = {23},
     number = {2},
     doi = {10.4171/ifb/453},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/453/}
}
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