By means of the Laplace transform method sufficient conditions for the existence of exponentially decaying memory kernels in heat flow and viscoelasticity are derived solving corresponding inverse problems. The observation functionals of the inverse problems are built up by n eigenfunctions of the related elliptic equation or the data of the direct problems possess n non-vanishing Fourier coefficients, only. In the special cases n = 1 and n = 2 the Laplace transforms of the memory kernel are given in explicit form.
This journal presents original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published.