带极大单调图的半线性抛物型方程的零能控性(英文)  

Null Controllability of Semilinear Parabolic Equation With Nonlinear Terms Involving a Maximal Monotone Graph

作　　者：张亮[1] 何朗[1] 

机构地区：[1]武汉理工大学理学院数学系,武汉湖北430070

出　　处：《数学进展》2011年第1期11-22,共12页Advances in Mathematics（China）

基　　金：supported by NSFC(No.10726031,No.10801057);the Fundamental Research Funds for the Central Universities

摘　　要：本文讨论非线性项带一个极大单调图的半线性抛物型方程系统的零能控性.文中利用Kakutani不动点定理和线性抛物型方程的能控性得到该系统是零能控的,如果控制作用在内部区域上.由此,还得到该系统是零能控的,如果控制施加在一部分边界上.This work concerns the null controllability of the system governed by semilinear parabolic equation with nonlinearity involving a bounded maximal monotone graph.We obtain by the Kakutani＇s fixed point theorem and the associated controllability for linear parabolic equations that the system is null controllable in the case when control acts in a subdomain.As a consequence,we also obtain that the system is null controllable when control acts on a portion of the boundary.

关 键 词：零能控 CARLEMAN不等式 极大单调图 

分 类 号：O231.4[理学—运筹学与控制论] O232[理学—数学]