Flow-invariant closed sets with respect to nonlinear semigroup flows

被引：10

作者：

Barbu, V

Pavel, NH ^{[1
]}

机构：

[1] Univ Iasi, Iasi 6600, Romania

[2] Ohio Univ, Dept Math, Athens, OH 45701 USA

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2003年 / 10卷 / 01期

关键词：

nonlinear semigroup generators; flow invariant sets; tangential (contingent) cones; divergence; gradients; curl; Sobolev spaces; Enstrophy and Helicity sets; Navier-Stokes equations;

D O I：

10.1007/s00030-003-1023-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A general result on the flow-invariance of a closed subset with respect to a differential equation associated with a nonlinear semigroup generator on Banach spaces is given. Applications to the flow-invariance of controlled flux sets (including the Enstrophy and Helicity sets) with respect to semilinear parabolic equations and Navier-Stokes equations are given.

引用

页码：57 / 72

页数：16

共 11 条

[1]

Arnold V. I., 1998, TOPOLOGICAL METHODS

[2]

Barbu V., 1975, NONLINEAR SEMIGROUPS

[3]

BARBU V, IN PRESS J MATH ANAL

[4] ON A CHARACTERIZATION OF FLOW-INVARIANT SETS [J].