Inverse problems for identification of memory kernels in thermo- and poro-viscoelasticity

Abstract

Inverse problems for identification of the four memory kernels in one-dimensional linear thermoviscoelasticity are reduced to a system of non-linear Volterra integral equations using Fourier's method for solving the direct problem. To this system of equations the contraction principle in weighted norms is applied. In this way global in time existence of a solution to the inverse problems is proved and stability estimates for it are derived. In analogous way inverse problems for the memory kernels in linear poroviscoelasticity can be handled. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.