Heat Conduction and the Mean Curvature Flow on the Whole Space

DOI Web Site 30 References

Bibliographic Information

Other Title
  • 全空間における熱伝導現象と平均曲率流運動
  • ゼン クウカン ニ オケル ネツ デンドウ ゲンショウ ト ヘイキンキョクリツ リュウウンドウ

Search this article

Description

We studied the heat conduction and the mean curvature flow in the whole space. In the initial problem for the heat equation in the whole space, the solution does not necessarily converge to any fixed values as time goes to infinity, even if we consider bounded initial values. Recently it is shown that the same phenomenon occurs in the curvature flow problem and, more precisely, that the large time behavior of solutions of these two equations are equivalent under some assumptions on the initial value. To understand this fact, we introduced a technique for analyzing parabolic equations as the heat equation with some heat flux.

Journal

References(30)*help

See more

Details 詳細情報について

Report a problem

Back to top