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- W1968266061 abstract "In this paper we consider the heat equation with memory in a bounded region $Omega subsetmathbb{R}^d$, $dgeq 1$, 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." @default.
- W1968266061 created "2016-06-24" @default.
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- W1968266061 date "2014-04-10" @default.
- W1968266061 modified "2023-09-27" @default.
- W1968266061 title "Approximate controllability and lack of controllability to zero of the heat equation with memory" @default.
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- W1968266061 doi "https://doi.org/10.48550/arxiv.1404.2745" @default.
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