Remarks on non controllability of the heat equation with memory

Abstract

Abstract. In this paper we deal with the null controllability problem for the heat equation with a memory term by means of boundary controls. For each positive final time T and when the control is acting on the whole boundary, we prove that there exists a set of initial conditions such that the null controllability property fails.Mathematics Subject Classification. 93B.

Stabilization of semilinear heat equations, with fading memory, by boundary feedbacks

“…Finally, we remark the very recent result on the present subject in [19], well as the recent result in [9], concerning the stochastic version of the problem.…”

Approximate controllability of a parabolic integrodifferential equation

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“…We give an overview of some of the ideas used in this kind of study for systems of "hyperbolic" type, i.e. finite velocity of signal propagation (the "parabolic" case is far less studied, see [8,37,[41][42][43]): operator methods (introduced by Belleni-Morante in [10] and used for control problems in [74]) are in Chap. 2; a moment method approach to controllability is in Chap.…”