scholarly journals Boundary behavior of positive solutions of the heat equation on a semi-infinite slab

1986 ◽  
Vol 295 (2) ◽  
pp. 687-687
Author(s):  
B. A. Mair
Keyword(s):  
Heat Equation ◽  
Positive Solutions ◽  
Boundary Behavior ◽  
Infinite Slab

Gradient and Harnack-type estimates for PageRank

2020 ◽  
pp. 1-19
Author(s):  
Paul Horn ◽  
Lauren M. Nelsen
Keyword(s):  
Heat Equation ◽  
Positive Solutions ◽  
Gradient Estimate ◽  
Personalized Pagerank ◽  
Geometric Properties ◽  
Algorithmic Design

Abstract Personalized PageRank has found many uses in not only the ranking of webpages, but also algorithmic design, due to its ability to capture certain geometric properties of networks. In this paper, we study the diffusion of PageRank: how varying the jumping (or teleportation) constant affects PageRank values. To this end, we prove a gradient estimate for PageRank, akin to the Li–Yau inequality for positive solutions to the heat equation (for manifolds, with later versions adapted to graphs).

scholarly journals Initial trace of positive solutions of a class of degenerate heat equation with absorption

2013 ◽  
Vol 33 (5) ◽  
pp. 2033-2063 ◽  
Author(s):  
Tai Nguyen Phuoc ◽  
◽  
Laurent Véron ◽  
Keyword(s):  
Heat Equation ◽  
Positive Solutions

scholarly journals A local Hopf lemma for solutions of the one dimensional heat equation

1997 ◽  
Vol 146 ◽  
pp. 1-12
Author(s):  
Noriaki Suzuki
Keyword(s):  
Heat Equation ◽  
Finite Order ◽  
Boundary Point ◽  
Local Minimum ◽  
Boundary Behavior ◽  
Lateral Boundary ◽  
Temperature Function ◽  
One Dimensional ◽  
The One

Abstract.The boundary behavior of solutions of the heat equation (temperature functions) is investigated. It is proved that a temperature function is identically equal to zero if it vanishes of finite order at some lateral boundary point where it attains a local minimum.

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