Solving inverse problems in relaxation experiments

Inverse problems of performing integral transforms with kernels depending on the division or product of arguments are considered in the study of linear viscoelastic behaviour of solid materials. Mechanism of arising instability of the solution is disclosed. An approach of solving the inverse problems is proposed by combining the logarithmic transformation of signal scale with digital filtering and utilizing sampling as a regularization tool to minimize output error. As an example, inherently ill-conditioned problem of the relaxation analysis is considered.