Large time behavior of the heat kernel

摘要

In this paper we study the large time behavior of the (minimal) beat kernel k(P)(M) (x, y, t) of a general time-independent parabolic operator Lu = u(t) + P(x, partial derivative(x))u which is defined on a. noncompact manifold M. More precisely, we prove that lim(t-->infinity) e(lambda0t) k(P)(M)(x, y, t) always exists. Here lambda(0) is the generalized principal eigenvalue of the operator P in M. (C) 2003 Elsevier Inc. All rights reserved. [References: 32]