固定点控抛物型方程的整体近似能控与有限维精确能控性(英文)

Global Approximately Controllability and Finite Dimensional Exact Controllability for Parabolic Equation with Fixed Point Controls

研究固定点控抛物型方程 : y(t,x) t =Δy -q(x)y(t,x) + Nk =1 vk(t)δ(x -xk) .证明了当特征值 ,特征函数及控制支撑点满足某些条件时系统的整体近似能控与有限维精确能控性 .

Parabolic equation with fixed point-controls:y(t,x)t=Δy-q(x)y(t,x)+ N k=1 v k(t)δ(x-x k) is studied.This system is globally approximately controllable and finite-dimensional exactly controllable when the eigenvalues,eigenfunctions and the points which support the controls satisfy some assumptions.