Abstract
In this paper we consider the analytic and numerical analysis of a class of inverse problems arising from input-output systems governed by partial differential equations of parabolic type where the inputs and outputs are given as point actuators and sensors. In particular, it is assumed that an unknown input produces an (approximately) known or desired output. The output is given as a finite set of data from which it is desired to (approximately) reconstruct the effecting input. It is well known that this type of scenario typically leads to ill-posed problems about which there is a vast literature.
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Gilliam, D.S., Lund, J.R., Mair, B.A., Martin, C.F. (1991). A Regularization Method for Inverse Heat Conduction Problems. In: Bowers, K., Lund, J. (eds) Computation and Control II. Progress in Systems and Control Theory, vol 11. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0427-5_10
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DOI: https://doi.org/10.1007/978-1-4612-0427-5_10
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