English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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 speedof the signal is infinite (i.e. the Colemann-Gurtin model). The memory kernelis of class $C^1$. We examine its controllability properties both under theaction of boundary controls or when the controls are distributed in a subregionof $\Omega$. We prove approximate controllability of the system and, incontrast with this, we prove the existence of initial conditions which cannotbe steered to hit the target $0$ in a certain time $T$, of course when thememory kernel is not identically zero. In both the cases we derive our resultsfrom well known properties of the heat equation.

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