Null control of heat equations with analytic memory kernels

TL;DR

This paper investigates the null controllability of heat equations with analytic memory kernels, extending previous results from polynomial kernels to more general analytic cases.

Contribution

It generalizes null controllability results from polynomial to analytic memory kernels in heat equations.

Findings

Null controllability holds for heat equations with polynomial memory kernels.

Extension of null controllability results to analytic memory kernels.

Control properties depend on the support covering the domain.

Abstract

We analyze the control properties of heat equations with memory terms. We recall previous results showing that if the moving support of the control covers the whole domain where heat diffuses, the system is null controllable when the memory kernel is polynomial. We formulate the problem of extending this result to the case of some more general memory kernels, in particular analytic ones.