树上生灭过程收敛速度及p-Laplacian特征值估计

项目名称： 树上生灭过程收敛速度及p-Laplacian特征值估计

项目编号： No.11526075

项目类型： 专项基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 王玲娣

作者单位： 河南大学

项目金额： 2.6万元

中文摘要： 本项目主要研究树上生灭过程的收敛速度和p-Laplacian主特征值的定量估计问题。 首先,从Poisson方程出发，利用变分公式、对偶方法等研究树上生灭过程的收敛速度估计问题, 也即 p=2时p-Laplacian特征值估计；其次,借鉴树上生灭过程收敛速度的方法，以泛函不等式为工具，研究p-Laplacian特征值(1

中文关键词： 马氏过程；生灭过程；收敛速度；p-Laplacian 特征值；

英文摘要： The program is proposed to investigate the estimates of coverage speed for birth-death processes on trees and p-Laplacian principal eigenvalues. Firstly, we study the coverage speed for birth-death processes on trees by taking advantage of variational formulas and dual methods. That is the p-Laplacian principal eigenvalues with p=2. Secondly, we will estimate the p-Laplacian(1<p<\infty) principal eigenvalues on trees by functional inequalities. These contents studied can be fully considered by comparing them with corresponding results obtained for birth-death processes in dimension one. In order to overcome the difficulties encountered duo to the changes of the Topo structure, we can consider the simple cases first, and then the general cases, splitting technic and so on. We know that the p-Laplacian eigenvalues are closely related to the best constant of functional inequalities, to some extent, the contents studies in the program complement the gap of estimating the best constant of functional inequalities. Besides, a cutoff phenomenon which is useful for algorithm designed in web and so on are closely related to the coverage speed. The research contents of this project from the theory to applications have important value.

英文关键词： Markov process;；birth and death process；convergence rate；p-Laplacian eigenvalue；