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We consider a distributed system of a type which is encountered in the study of diffusion processes with memory and in viscoelasticity. The key feature of such a system is the persistence in the future of the past actions due the memory described via a certain  relaxation kernel;  see below. The parameters of the kernel have to be inferred from experimental measurements. Our main result in this paper is that by using two boundary measurements, the identification of a relaxation kernel which is a linear combination of  Abel kernels  (as often assumed in applications) can be reduced to the solution of a  (linear) deconvolution problem.

A linear algorithm for the identification of a weakly singular relaxation kernel using two boundary measurements