AN INVERSE CONVOLUTION METHOD FOR REGULAR PARABOLIC EQUATIONS

In this paper, the problem of determining an unknown boundary control of a parabolic distributed parameter system, evolving over finite or infiinte time, from incomplete, approximate interior temperature measurements is investigated. First, an exact solution is obtained for square integrable boundary controls associated with a general class of parabolic equations on a finite spatial interval under the assumption that the interior temperature is known for all times. Then, it is shown that this exact solution can be used to develop a stable algorithm for the numerical solution of this problem, without the introduction of standard regularization techniques. This algorithm assumes only knowledge of a finite, discrete set of approximate temperature readings. One advantage of this inversion process is the availability of a priori error bounds based on the measurement errors and frequency of sampling that are obtained in this paper. Another useful feature is that it encompasses boundary controls which are arbitrary linear combinations of surface temperature and flux. Numerical results are presented.