This article is cited in 2 papers

The logarithmic gradient of the Kernel of the heat equation with drift on a Riemannian manifold

Yu. N. Bernatskaya

National Technical University of Ukraine "Kiev Polytechnic Institute"

Abstract: For a parabolic equation with drift on a Riemannian manifold of positive curvature we obtain a representation for the logarithmic gradient in the form of the sum of two vector fields one of which is known and the other is bounded. The drift field is assumed to be of sufficiently rapid decay at infinity.

Keywords: fundamental solution, Riemannian manifold, Laplace–Beltrami operator, vector field.

UDC: 517.9:514.7

Received: 11.04.2003

 English version: Siberian Mathematical Journal, 2004, 45:1, 11–18

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