We consider a model for the heat equation with memory, which has infinite propagation speed, like the standard heat equation. We prove that, in spite of this, for every T > 0 there exist square integrable initial data which cannot be steered to hit zero at time T , using square integrable controls. We show that the counterexample we present complies with the restrictions imposed by the second principle of thermodynamics.
Lack of controllability of the heat equation with memory / Andrei, Halanay; Pandolfi, Luciano. - In: SYSTEMS & CONTROL LETTERS. - ISSN 0167-6911. - STAMPA. - 61:(2012), pp. 999-1002. [10.1016/j.sysconle.2012.07.002]
Lack of controllability of the heat equation with memory
PANDOLFI, LUCIANO
2012
Abstract
We consider a model for the heat equation with memory, which has infinite propagation speed, like the standard heat equation. We prove that, in spite of this, for every T > 0 there exist square integrable initial data which cannot be steered to hit zero at time T , using square integrable controls. We show that the counterexample we present complies with the restrictions imposed by the second principle of thermodynamics.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2502213
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