Large time behavior of the heat kernel

2002/06/26 by Yehuda Pinchover, Pinchover, Yehuda
Computer Science · Mathematics · #35B40 #35K10 #58J35 #60J60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Probability (math.PR) #math.AP #math.PR #msc:35B40 #msc:35K10 #msc:58J35 #msc:60J60

paper · pdf · doi:10.48550/arxiv.math/0206281

15 pages

arxiv created 2002/06/26 · openalex publication_date 2002/06/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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, ∂_x) which is defined on a noncompact manifold M. More precisely, we prove that lim_t→∞ e^{λ₀ t}k_P^M(x,y,t) always exists. Here λ₀ is the generalized principal eigenvalue of the operator P in M.

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