Some identification problems related to thermal materials with loss of memory

Il contributo è un articolo scientifico originale, non pubblicato altrove in nessuna forma. The author considers a new class of identification problems for integro-differential parabolic equations describing the evolution of the temperature in a material with memory. The memory effects are taken into account by convolution kernels that are in general unknown. There is a large body of literature for identification problems consisting in determining both the temperature and the convolution memory kernel with the assumption that additional measurements on the temperature are taken into account. The new problem the author considers is the determination of a suitable additional function (together with the temperature and the convolution memory kernel) that appears in one of the extremes of integration, that is, in the convolution integral of the evolution equation of the temperature. This term takes into account the loss of memory of the material. In the references of the paper we find the motivation for the study of such new problems.