A linear algorithm for the identification of a relaxation kernel using two boundary measures

We consider a distributed system with persistent memory of a type which is encountered in the study of diffusion processes with memory and viscoelasticity for materials of Maxwell-Boltzmann type. relaxation kernel, i.e. the kernel of the memory term, is scarcely known from first principles, and it has to be inferred from experiments taken on samples of the material. We prove that \emph{two boundary measures} give a \emph{linear } Volterra integral equation of the first kind for the unknown kernel. Hence, with two measures, the identification of the kernel, which in principle is a nonlinear problem, is reduced to the solution of a deconvolution problem, hence to an ill posed but linear problem which can be solved with existing methods.