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oaioai:iris.polito.it:11583/2502213

Lack of controllability of the heat equation with memory

Authors
Publication date
1 January 2012
Publisher
Elsevier BV:PO Box 211, 1000 AE Amsterdam Netherlands:011 31 20 4853757, 011 31 20 4853642, 011 31 20 4853641, EMAIL: [email protected], INTERNET: http://www.elsevier.nl, Fax: 011 31 20 4853598
Doi

    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

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