Approximate controllability and lack of controllability to zero of the heat equation with memory

L. Pandolfi; A. Halanay

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arXiv · 1404.2745

Approximate controllability and lack of controllability to zero of the heat equation with memory

L. Pandolfi·A. Halanay

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Abstract

In this paper we consider the heat equation with memory in a bounded region $\Omega \subset\mathbb{R}^d$, $d\geq 1$, in the case that the propagation speed of the signal is infinite (i.e. the Colemann-Gurtin model). The memory kernel is of class $C^1$. We examine its controllability properties both under the action of boundary controls or when the controls are distributed in a subregion of $\Omega$. We prove approximate controllability of the system and, in contrast with this, we prove the existence of initial conditions which cannot be steered to hit the target $0$ in a certain time $T$, of course when the memory kernel is not identically zero. In both the cases we derive our results from well known properties of the heat equation.

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BibTeX RIS

L. Pandolfi, A. Halanay. 2014-04-10. Approximate controllability and lack of controllability to zero of the heat equation with memory. https://arxiv.org/abs/1404.2745

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