Point control: approximations of parabolic problems and pseudo parabolic problems

Abstract

We consider quadratic control problems in which the underlying equation is of parabolic or pseudo-parabolic type and the distributed control is a Dirac-like function. The following approximating properties are studied i) the equation is fixed and the controls converge to a delta function and ii) the type of control is fixed and the pseudo-parahollc equations formally ,approach the parabolic

AMS (MOS) Subject Classification (1970):

• Primary 49A20
• 49B25

Keywords:

• Pseudo-parabolic equation
• point control

^†This research was supported in part by National Science foundation Grant No. MCS-7902037 and a University of Oklahoma Energy Resuources Center fellowship

^†This research was supported in part by National Science foundation Grant No. MCS-7902037 and a University of Oklahoma Energy Resuources Center fellowship

Notes

^†This research was supported in part by National Science foundation Grant No. MCS-7902037 and a University of Oklahoma Energy Resuources Center fellowship