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The logarithmic gradient of the kernel of the heat equation with drift on a Riemannian manifold. (Russian, English) Zbl 1125.58008
Sib. Mat. Zh. 45, No. 1, 16-24 (2004); translation in Sib. Math. J. 45, No. 1, 11-18 (2004).
Summary: 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.
MSC:
58J35 Heat and other parabolic equation methods for PDEs on manifolds
35A08 Fundamental solutions to PDEs
35K55 Nonlinear parabolic equations
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