Point control: approximations of parabolic problems and pseudo parabolic problems

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

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