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IMA Journal of Mathematical Control and Information 1994 11(2):169-183; doi:10.1093/imamci/11.2.169
© 1994 by Institute of Mathematics and its Applications
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On the inversion and simulation of the heat equation

MOHAMMED A. SARHAN

Department of Electrical Engineering and Computer Science, University of Wisconsin Milwaukee, WI 53201–0784, U.S.A.

We consider a heat equation in one dimension with a boundary input and distributed output. An approximate inverse for the input—output system described by this model is developed. The inverse is obtained by Galerkin approximation either (1) before or (2) after inversion. An estimate of the error due to the approximation is established for the two cases. In addition, Fourier-series expansion is used to compare these inversion methods.


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