抄録
The purpose of this paper is to study some optimal boundary control problem with boundary observation in second order parabolic systems, where control and observation are performed in a pointwise way, respectively.
Pointwise controls are defined using a scalar multiple of the Dirac measure under the Neumann boundary condition. Pointwise observations are introduced using characteristic functions at observation points.
Results obtained are as follows: (1) In pointwise boundary control and -observation systems, both the control and observation can not be defined at the same time by Dirac measure; (2) If pointwise boundary control is defined by Dirac measure, the adjoint state will be reduced to a complicated system involving the Laplace-Beltrami operator.
