Large time behavior of the heat kernel

Details Large time behavior of the heat kernel Large time behavior of the heat kernel

2002-06-26

arxiv.org/abs/math/0206281v1

Mathematics

Analysis of PDEs

15 pages

Scientific paper

In this paper we study the large time behavior of the (minimal) heat kernel $k_P^M(x,y,t)$ of a general time independent parabolic operator $L=u_t+P(x, \partial_x)$ which is defined on a noncompact manifold $M$. More precisely, we prove that $$\lim_{t\to\infty} e^{\lambda_0 t}k_P^{M}(x,y,t)$$ always exists. Here $\lambda_0$ is the generalized principal eigenvalue of the operator $P$ in $M$.

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