Uniqueness and nonuniqueness of the positive Cauchy problem for the heat equation on Riemannian manifolds
Uniqueness and nonuniqueness of the positive Cauchy problem for the heat equation on Riemannian manifolds
复制标题
黎曼流形上热方程正柯西问题的唯一性和非唯一性
DOI：
10.1090/s0002-9939-1995-1242097-3
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
M. Murata
中科院分区：
文献类型：
--
作者：
M. Murata
研究了非紧黎曼流形上热方程的非负解是否由其初始数据唯一确定的唯一性问题。唯一性的充分条件。非唯一性是用非可积性的形式给出的。在无穷远处的可积性（-1）乘以一个负函数。歧管的截面曲率从下面有界（相对而言）。（上图）。对于一类流形，这些充分条件给出了唯一性的一个简单判据。
We investigate a uniqueness problem of whether a nonnegative solution of the heat equation on a noncompact Riemannian manifold is uniquely determined by its initial data. A sufficient condition for the uniqueness (resp. nonuniqueness) is given in terms of nonintegrability (resp. integrability) at infinity of -1 times a negative function by which the Ricci (resp. sectional) curvature of the manifold is bounded from below (resp. above) at infinity. For a class of manifolds, these sufficient conditions yield a simple criterion for the uniqueness.