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Asymptotic behaviour to a heat equation with a delayed control in the source term

Berrone L., Mannucci P.

Control and Cybernetics

2004

Vol. 33, no 1

5-32

A one dimensional heat equation in a semi-infinite medium controlled through a heat source depending on the delayed heat flux at the extremum is studied. By reducing the problem to a delayed Volterra integral equation with a weakly singular kernel, we find conditions on the initial datum and on the source term of the equation to control the asymptotic behaviour of the mean temperatures.