ON A CONTROL PROBLEM FOR MEMORY KERNELS IN HEAT-CONDUCTION

A problem of identification of memory kernels in heat flow in a bar consisting of material with thermal memory is considered. The corresponding linear integrodifferential equation for the temperature contains a pair of time-dependent convolution kernels that are unknown. Such kernels are determined as solutions of an optimal control problem of least squares type by using additional data obtained from measurements of temperature in fixed points of the bar over some finite time interval. We derive optimality conditions for the memory kernels and give a numerical example for constructing them.