Abstract.
The main result we derive is the proof that a particular set of functions related to the controllability of the heat equation with memory and finite signal speed, with suitable kernel, is a Riesz system. Riesz systems are important tools in applied mathematics, for example for the solution of inverse problems. In this paper we shows that the Riesz system we identify can be used to give a constructive method for the computation of the control steering a given initial condition to a prescribed target.
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Pandolfi, L. Riesz Systems and Controllability of Heat Equations with Memory. Integr. equ. oper. theory 64, 429–453 (2009). https://doi.org/10.1007/s00020-009-1682-1
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DOI: https://doi.org/10.1007/s00020-009-1682-1