Uniqueness and Nonuniqueness of the Positive Cauchy Problem for the Heat Equation on Riemannian Manifolds

Minoru Murata
1995 Proceedings of the American Mathematical Society  
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
more » ... se sufficient conditions yield a simple criterion for the uniqueness.
doi:10.2307/2161012 fatcat:leleapshy5gmdisw6abyyv2eoa