全空間における熱伝導現象と平均曲率流運動

概要

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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.
日本応用数理学会の論文
2009-03-25