Stability in the almost everywhere sense: A linear transfer operator approach

被引：39

作者：

Rajaram, R. ^{[1
]}

Vaidya, U. ^{[2
]}

Fardad, M. ^{[3
]}

Ganapathysubramanian, B. ^{[4
]}

机构：

[1] Kent State Univ, Dept Math Sci, Ashtabula, OH 44004 USA

[2] Iowa State Univ, Dept Elec & Comp Engn, Ames, IA 50011 USA

[3] Syracuse Univ, Dept Elec Engn & Comp Sci, Syracuse, NY 13244 USA

[4] Iowa State Univ, Dept Mech Engn, Ames, IA 50011 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 368卷 / 01期

关键词：

Almost everywhere stability; Advection equation; Density function;

D O I：

10.1016/j.jmaa.2010.02.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The problem of almost everywhere stability of a nonlinear autonomous ordinary differential equation is studied using a linear transfer operator framework. The infinitesimal generator of a linear transfer operator (Perron-Frobenius) is used to provide stability conditions of an autonomous ordinary differential equation. It is shown that almost everywhere uniform stability of a nonlinear differential equation, is equivalent to the existence of a non-negative solution for a steady state advection type linear partial differential equation. We refer to this non-negative solution, verifying almost everywhere global stability, as Lyapunov density. A numerical method using finite element techniques is used for the computation of Lyapunov density. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：144 / 156

页数：13